Application of Tikhonov’s theorem for automatic stabilization of controlled motion

A decomposition of a control algorithm is proposed in the form of a combination of control laws for the slow and fast variables of a controlled system. This is possible due to the fulfilment of Tikhonov’s theorem hypotheses for singularly perturbed systems.     

Global reactivity indexes and nonparametric statistics in the study of the proapoptotic activity of coumarins

Coumarins are widely distributed as secondary metabolites and are popular structural motifs among known anticancer agents; their planarity and electronic environment are very important building blocks for bioactive compounds. Due to the broad scope of their biological activity, anticancer properties of these molecules remain an important goal for medicinal chemistry. In this work, the knowledge and understanding of the correlation between electronic environment and global reactivity of a series of hydroxycoumarins lead to develop a statistical model to study the proapoptotic activity of this type of compounds. Thus, the analysis of the charge distribution within the molecule and experimental data of proapoptotic activity of known coumarins are analyzed through a regression model. This model offers the possibility of predicting whether a structural related coumarin will show the desired activity or not, which increases the ability to a target-directed approach in the development of anticancer therapeutic agents.     

Analytical Solution for Multi-Species Contaminant Transport in Finite Media with Time-Varying Boundary Conditions

Most analytical solutions available for the equations governing the advective–dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this study, we present an analytical solution for a finite domain and a time-varying boundary condition. The solution was found using the Classic Integral Transform Technique (CITT) in combination with a filter function having separable space and time dependencies, implementation of the superposition principle, and using an algebraic transformation that changes the advection–dispersion equation for each species into a diffusion equation. The analytical solution was evaluated using a test case from the literature involving a four radionuclide decay chain. Results show that convergence is slower for advection-dominated transport problems. In all cases, the converged results were identical to those obtained with the previous solution for a semi-infinite domain, except near the exit boundary where differences were expected. Among other applications, the new solution should be useful for benchmarking numerical solutions because of the adoption of a finite spatial domain.     

Synthesis of acetimino complexes of Pt(II) and Pt(IV) and the first heteronuclear mu-acetimido complexes

The reactions of [Ag(NH=CMe2)2]ClO4 with cis-[PtCl2L2] in a 1:1 molar ratio give cis-[PtCl(NH=CMe2)(PPh3)2]ClO4 (1cis) or cis-[PtCl(NH=CMe2)2(dmso)]ClO4 (2), and in 2:1 molar ratio, they produce [Pt(NH=CMe2)2L2](ClO4)2 [L = PPh3 (3), L2= tbbpy = 4,4'-di-tert-butyl-2,2'-dipyridyl (4)]. Complex 2 reacts with PPh3 (1:2) to give trans-[PtCl(NH=CMe2)(PPh3)2]ClO(4) (1trans). The two-step reaction of cis-[PtCl2(dmso)2], [Au(NH=CMe2)(PPh3)]ClO4, and PPh3 (1:1:1) gives [SP-4-3]-[PtCl(NH=CMe2)(dmso)(PPh3)]ClO4 (5). The reactions of complexes 2 and 4 with PhICl2 give the Pt(IV) derivatives [OC-6-13]-[PtCl3(NH=CMe2)(2)(dmso)]ClO4 (6) and [OC-6-13]-[PtCl2(NH=CMe2)2(dtbbpy)](ClO4)2 (7), respectively. Complexes 1cis and 1trans react with NaH and [AuCl(PPh3)] (1:10:1.2) to give cis- and trans-[PtCl{mu-N(AuPPh3)=CMe2}(PPh3)2]ClO4 (8cis and 8trans), respectively. The crystal structures of 4.0.5Et2O.0.5Me2CO and 6 have been determined; both exhibit pseudosymmetry.     

Geometrical Aspects of Lie Group Representations and Their Optical Applications

A new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group) is presented. Some applications of the construction in quantumoptics problems are discussed. The notion of phase space of a Lie group is studied. The possibility of describing the quadrature components of a photon, in view of the Lie group phase space, is pointed out. Examples of two and threedimensional Lie groups including Heisenberg–Weyl group are considered.     

Spectrally-resolved white-light interferometry as a profilometry tool

Phase-shifting interferometry and white-light interferometry are reliable techniques for surface analysis in which the optical path difference has to be changed by some transducer to evaluate the phase. We present here a different procedure in which optical path modulation is completely avoided. This technique is based on the spectral analysis of white-light interferograms. By means of a spectroscopic device, a non-visible interferogram is split into its monochromatic components and absolute, unambiguous values of the phase are obtained along the spectral axis. Only one interferogram is required to obtain the profile of one-dimensional surfaces with nanometric resolution.