859 research outputs found
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
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