Asymmetric Hydrogenation in Water by a Rhodium Complex of Sulfonated 2,2'-Bis(diphenylphosphino)-1,1'-binaphthyl (binap)

The synthesis of sulfonated 2,2′-bis(diphenylphosphino)-1,1′-binaphthyl (binap) is reported; a rhodium complex of this ligand is the first to perform asymmetric hydrogenation in neat water with optical yields as high as those obtained in nonaqueous solvent

Counting Value Sets: Algorithm and Complexity

Let $p$ be a prime. Given a polynomial in \F_{p^m}[x] of degree $d$ over the finite field \F_{p^m}, one can view it as a map from \F_{p^m} to \F_{p^m}, and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on computing the cardinality of this value set. We show an elementary connection between this cardinality and the number of points on a family of varieties in affine space. We then apply Lauder and Wan's $p$-adic point-counting algorithm to count these points, resulting in a non-trivial algorithm for calculating the cardinality of the value set. The running time of our algorithm is $(pmd)^{O(d)}$. In particular, this is a polynomial time algorithm for fixed $d$ if $p$ is reasonably small. We also show that the problem is #P-hard when the polynomial is given in a sparse representation, $p=2$, and $m$ is allowed to vary, or when the polynomial is given as a straight-line program, $m=1$ and $p$ is allowed to vary. Additionally, we prove that it is NP-hard to decide whether a polynomial represented by a straight-line program has a root in a prime-order finite field, thus resolving an open problem proposed by Kaltofen and Koiran in \cite{Kaltofen03,KaltofenKo05}

Universality of the edge tunneling exponent of fractional quantum Hall liquids

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $\nu = 1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.Comment: 5 pages, 3 figure

The equivariant K-theory of toric varieties

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this result is established in a more general context, involving the K-theory of graded projective modules. The second result is a new proof of a theorem due to Vezzosi and Vistoli concerning the equivariant K-theory of smooth (not necessarily affine) toric varieties.Comment: 12 page

Robust Half-Metallic Character and Large Oxygen Magnetism in a Perovskite Cuprate

The new perovskite cuprate material Sr$_{8}$CaRe$_{3}$Cu$_{4}$O$_{24}$, which behaves ferrimagnetically and shows an unusually high Curie temperature ($T_c \sim$ 440 K), is found from density-functional theory calculation to display several surprising properties after hole doping or chemical substitution: (1) Half metal (HM) is realized by replacing Re with W or Mo while $T_c$ remains high; (2) hole-doped Sr$_{8}$CaRe$_{3}$Cu$_{4}$O$_{24}$ is also HM with high $T_c$. Moreover, we find that the O atoms will carry a large magnetic moment after hole doping, which is in sharp contrast with the generally accepted concept that magnetism in solid requires partially filled shells of $d$ or $f$ electrons in cations. The material Sr$_8$CaRe$_3$Cu$_4$O$_{24}$ is therefore expected to provide a very useful platform for material design and development.Comment: 5 pages and 4 figure

Enhancement of Dark Matter Annihilation via Breit-Wigner Resonance

The Breit-Wigner enhancement of the thermally averaged annihilation cross section is shown to provide a large boost factor when the dark matter annihilation process nears a narrow resonance. We explicitly demonstrate the evolution behavior of the Breit-Wigner enhanced as the function of universe temperature for both the physical and unphysical pole cases. It is found that both of the cases can lead an enough large boost factor to explain the recent PAMELA, ATIC and PPB-BETS anomalies. We also calculate the coupling of annihilation process, which is useful for an appropriate model building to give the desired dark matter relic density.Comment: 4 pages, 4 figures, references added, accepted for publication in Physical Review

Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $\nu = 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.Comment: 4 pages, 3 figures. New version shortened for PRL. Corrected typo