Some minimization problems for the free analogue of the Fisher information

We consider the free non-commutative analogue Phi^*, introduced by D. Voiculescu, of the concept of Fisher information for random variables. We determine the minimal possible value of Phi^*(a,a^*), if a is a non-commutative random variable subject to the constraint that the distribution of aa^* is prescribed. More generally, we obtain the minimal possible value of Phi^*({a_{ij},a_{ij}^*), if {a_{ij}} is a family of non-commutative random variables such that the distribution of AA^* is prescribed, where A is the matrix (a_{ij}). The d*d-generalization is obtained from the case d=1 via a result of independent interest, concerning the minimal value of Phi^*({a_{ij},a_{ij}^*), when the matrix A=(a_{ij}) and its adjoint have a given joint distribution. We then show how the minimization results obtained for Phi^* lead to maximization results concerning the free entropy chi^*, also defined by Voiculescu.Comment: 31 pages, Late

Development and validation of a RP- HPLC method for the quantitation studies of bromadiolone in Ratitox F

An isocratic high-performance liquid chromatography (HPLC) procedure was developed for the quantitative determination of bromadiolone (hydroxycoumarins) in Ratitox F product – rodenticide. HPLC separation was carried out by reversed phase chromatography ODS 2 Hypersil C18 (250 mm x 4.6 mm i.e.; 5 ìm particle size), held in thermostat at 25°C. The mobile phase consisted of methanol/0.1% aqueous solution phosphoric acid (90/10v/v), with a flow rate of 1 ml/min and with UV detection at 265 nm. In order to validate the method, the following parameters have been investigated- linearity (r2 = 0.9999), range, precision, accuracy, specificity, limit of detection and limit of quantification. The described method can be successfully applied for the analysis of Ratitox F – rodenticide

Density of States of Quantum Spin Systems from Isotropic Entanglement

We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.Comment: 4+ pages, content is as in the published versio

Measurement of the half-life of 198Au in a non-metal: High-precision measurement shows no host-material dependence

We have measured the half-life of the beta decay of 198Au to be 2.6948(9) d, with the nuclide sited in an insulating environment. Comparing this result with the half-life we measured previously with a metallic environment, we find the half-lives in both environments to be the same within 0.04%, thus contradicting a prediction that screening from a "plasma" of quasi-free electrons in a metal increases the half-life by as much as 7%

Complete diagrammatics of the single ring theorem

Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators. We also rederive the Haagerup-Larsen theorem and show how its recent extension to the eigenvector correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio