Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Probing the cosmic distance-duality relation with the Sunyaev-Zel'dovich effect, X-ray observations and supernovae Ia

Context. The angular diameter distances toward galaxy clusters can be determined with measurements of Sunyaev-Zel'dovich effect and X-ray surface brightness combined with the validity of the distance-duality relation, D-L(z)(1 + z)(2)/D-A(z) = 1, where D-L(z) and D-A(z) are, respectively, the luminosity and angular diameter distances. This combination enables us to probe galaxy cluster physics or even to test the validity of the distance-duality relation itself. Aims. We explore these possibilities based on two different, but complementary approaches. Firstly, in order to constrain the possible galaxy cluster morphologies, the validity of the distance-duality relation (DD relation) is assumed in the Lambda CDM framework (WMAP7). Secondly, by adopting a cosmological-model-independent test, we directly confront the angular diameters from galaxy clusters with two supernovae Ia (SNe Ia) subsamples (carefully chosen to coincide with the cluster positions). The influence of the different SNe Ia light-curve fitters in the previous analysis are also discussed. Methods. We assumed that eta is a function of the redshift parametrized by two different relations: eta(z) = 1 +eta(0)z, and eta(z) = 1 + eta(0)z/(1 + z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we considered the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical and spherical isothermal beta models and spherical non-isothermal beta model. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. For both approaches we find that the elliptical beta model agrees with the distance-duality relation, whereas the non-isothermal spherical description is, in the best scenario, only marginally compatible. We find that the two-light curve fitters (SALT2 and MLCS2K2) present a statistically significant conflict, and a joint analysis involving the different approaches suggests that clusters are endowed with an elliptical geometry as previously assumed. Conclusions. The statistical analysis presented here provides new evidence that the true geometry of clusters is elliptical. In principle, it is remarkable that a local property such as the geometry of galaxy clusters might be constrained by a global argument like the one provided by the cosmological distance-duality relation.

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Spectroscopic, Structural, and Conformational Properties of (Z)-4,4, 4-Trifluoro-3-(2-hydroxyethylamino)-1-(2-hydroxypheny1)-2-buten-1-one, C12H12F3NO3: A Trifluoromethyl-Substituted beta-Aminoenone

The ( Z)-4,4,4-trifluoro-3-(2-hydroxyethylamino)-1-(2-hydroxyphenyl)-2-buten-1-one (C12H12F3NO3) compound was thoroughly studied by IR, Raman, UV-visible, and C-13 and F-19 NMR spectroscopies. The solid-state molecular structure was determined by X-ray diffraction methods. It crystallizes in the P2(1)/c space group with a = 12.1420(4) angstrom, b = 7.8210(3) angstrom, c := 13.8970(5) angstrom, beta = 116.162(2)degrees, and Z = 4 molecules per unit cell. The molecule shows a nearly planar molecular skeleton, favored by intramolecular OH center dot center dot center dot 0 and NH center dot center dot center dot 0 bonds, which are arranged in the lattice as an OH center dot center dot center dot 0 bonded polymer coiled around crystallographic 2-fold screw-axes. The three postulated tautomers were evaluated using quantum chemical calculations. The lowest energy tautomer (I) calculated with density functional theory methods agrees with the observed crystal structure. The structural and conformational properties are discussed considering the effect of the intra- and intermolecular hydrogen bond interactions.

Shape isomerism and shape coexistence effects on the Coulomb energy differences in the N = Z nucleus As-66 and neighboring T=1 multiplets

Excited states of the N = Z = 33 nucleus As-66 have been populated in a fusion-evaporation reaction and studied using gamma-ray spectroscopic techniques. Special emphasis was put into the search for candidates for the T = 1 states. A new 3(+) isomer has been observed with a lifetime of 1.1(3) ns. This is believed to be the predicted oblate shape isomer. The excited levels are discussed in terms of the shell model and of the complex excited Vampir approaches. Coulomb energy differences are determined from the comparison of the T = 1 states with their analog partners. The unusual behavior of the Coulomb energy differences in the A = 70 mass region is explained through different shape components (oblate and prolate) within the members of the same isospin multiplets. This breaking of the isospin symmetry is attributed to the correlations induced by the Coulomb interaction.