Invariant integral and the transition to steady states in separable dynamical systems

We show that the transition between fixed points in a separable dynamical system is fully described by an invariant integral. We discuss in detail the case of a system with two temporal variables with bilinear coupling, where the new stable state is attained asymptotically through spiraling into the fixed point. Through the invariance, it is possible to establish conditions for the control parameter that permit a (targeted) transition in finite time and without relaxation oscillations.     

Fulfilling causality: two numerical techniques for accurately computing the propagation of independent laser beams through a nonlinear medium

We identify the origin of some numerical difficulties related to causality which appear in the simulation of transport equations. Two numerical techniques are presented for the integration of models describing counter-propagating laser beams in interaction with a nonlinear medium. One, based on the characteristic method, rests on the transport properties of first-order derivatives and is able to propagate a signal in a linear non-dispersive medium without any deformation. The other, fully explicit, directly handles both first and second order derivatives. Both numerical schemes are applied to a physical example. PACS 42.55.f; 42.60.Jf; 42.65.k; 42.65.Sf     

Stereochemical characterization of some mono- and diaryl substituted ethylene oxides by NMR spectroscopy

NMR spectra of several styrene, stilbene and stilbazole oxides have been determined, and chemical shifts and coupling constants have been correlated with cis-and trans-configurations. Assignments have been made for all protons, and double resonance technique and ¹³C? H coupling constants have been used in some particular cases. An explanation is proposed for the observation that chemical shifts of oxirane protons are higher for cis than for trans isomers.     

Optimal dimension reduction for high-dimensional and functional time series

Dimension reduction techniques are at the core of the statistical analysis of high-dimensional and functional observations. Whether the data are vector- or function-valued, principal component techniques, in this context, play a central role. The success of principal components in the dimension reduction problem is explained by the fact that, for any \(K\le p\), the K first coefficients in the expansion of a p-dimensional random vector \(\mathbf{X}\) in terms of its principal components is providing the best linear K-dimensional summary of \(\mathbf X\) in the mean square sense. The same property holds true for a random function and its functional principal component expansion. This optimality feature, however, no longer holds true in a time series context: principal components and functional principal components, when the observations are serially dependent, are losing their optimal dimension reduction property to the so-called dynamic principal components introduced by Brillinger in 1981 in the vector case and, in the functional case, their functional extension proposed by Hörmann, Kidziński and Hallin in 2015.     

A fully automated catecholamines analyzer based on cartridge extraction and HPLC separation

Summary A fully automated analyzer is described for the HPLC analysis of catecholamines. Firstly urinary and plasma catecholamines are reacted with diphenylboronic acid giving a complex without requiring a pH-meter step. This complex is strongly retained on a C 18 cartridge and elution with acetic acid solutions shows recoveries higher than 90 %. The catecholamines are eluted also by the mobile phase employed for the HPLC’ analysis. An intelligent autosampler makes the complex and fills a loop with all the solvents necessary for the sample cleanup. It then inverts the flow and pumps the sample and the solvents throught the cartridge. In the elution step the disposable extraction cartridge is positioned on stream with the HPLC analytical column by an automatic sampler. The separation is performed by ion-pair reversed-phase high-performance liquid chromatography, with sodium dodecyl sulphate as pairing ion, a short analytical column and electrochemical detection. The HPLC analysis time is 3 min and the total sample turnover time is 8 min. The recoveries and the precision of the analyzer are given together with correlation with manual HPLC.