Unusual Temperature-Retention Dependences Observed for Several Benzodiazepines in RP-HPLC Using Different Mobile Phase Compositions

Non-linear van’t Hoff plots were observed for several benzodiazepines over the usual temperature interval used in RP-LC (10–60 °C), when acetonitrile was added in the mobile phase. Such deviation from linearity was not observed when methanol or isopropanol was added to the mobile phase. Polynomial regressions were applied to fit the experimental data when acetonitrile was used as organic additive in mobile phase. The second-order polynoms may allow finding out the maximum retention depending on temperature, which can be within or out of the normal temperature range used in RP mechanism. A thermodynamic model deriving from the partition of two or more tautomers of the same analyte was proposed to explain this deviation from linearity of van’t Hoff plots.

     

Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki’s proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain (Prosen, in Phys Rev Lett 106:217206, 2011).     

Existence for a semilinear sixth-order ODE

In this paper we study the existence and multiplicity of nontrivial solutions for a boundary value problem associated with a semilinear sixth-order ordinary differential equation arising in the study of spatial patterns. Our treatment is based on variational tools, including two Brezis-Nirenberg's linking theorems.     

Bounded influence estimators for multivariate lognormal distributions

In this paper we consider the problem of robust estimation of some parameters related to a multivariate lognormal distribution. In this sense, we construct a class of estimators and discuss some of its properties, such as Fisher consistency, robustness and asymptotic normality. To cite this article: A. Toma, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Electroless formation of silver nanoaggregates: an experimental and molecular dynamics approach

The ability to manipulate matter to create non-conventional structures is one of the key issues of material science. The understanding of assembling mechanism at the nanoscale allows us to engineer new nanomaterials, with physical properties intimately depending on their structure.

This paper describes new strategies to obtain and characterise metal nanostructures via the combination of a top-down method, such as electron beam lithography, and a bottom-up technique, such as the chemical electroless deposition. We realised silver nanoparticle aggregates within well-defined patterned holes created by electron beam lithography on silicon substrates. The quality characteristics of the nanoaggregates were verified by using scanning electron microscopy and atomic force microscopy imaging. Moreover, we compared the experimental findings to molecular dynamics simulations of nanoparticles growth. We observed a very high dependence of the structure characteristics on the pattern nanowell aspect ratio. We found that high-quality metal nanostructures may be obtained in patterns with well aspect ratio close to one, corresponding to a maximum diameter of 50 nm, a limit above which the fabricated structures become less regular and discontinuous. When regular shapes and sizes are necessary, as in nanophotonics, these results suggest the pattern characteristics to obtain isolated, uniform and reproducible metal nanospheres.