Solutions of the average cost optimality equation for finite Markov decision chains: risk-sensitive and risk-neutral criteria

This work is concerned with controlled Markov chains with finite state and action spaces. It is assumed that the decision maker has an arbitrary but constant risk sensitivity coefficient, and that the performance of a control policy is measured by the long-run average cost criterion. Within this framework, the existence of solutions of the corresponding risk-sensitive optimality equation for arbitrary cost function is characterized in terms of communication properties of the transition law.     

Boron macrocycles having a calix-like shape. Synthesis, characterization, X-ray analysis, and inclusion properties

The syntheses, structure, and inclusion properties of trinuclear boron compounds having a calix-like shape are described. The compounds have been obtained via self-assembly reactions between salicylaldehyde derivatives and 3-aminophenylboronic acid, whereby the formation of three N --> B coordination bonds favored the oligomerization. The products have high melting points (>370 degrees C), are stable to moisture, and have good solubility in organic solvents; the latter property is useful for host-guest recognition experiments. The structural analysis by X-ray diffraction revealed that diverse conformations are possible because of the presence of two different units of aromatic rims. A cone-cone (double-cone) conformation is observed for three of these compounds, while the remaining one has a cone-partial cone conformation. An analysis of the molecular packing showed that the molecules are stacked in columns in two different orientations in relation to the organization of the macrocycles when referred to the N-B bonds. The inclusion properties toward primary amines and ammonium chlorides were analyzed by titration experiments and monitored by UV spectroscopy, whereby association constants on the order of 10(2)-10(3) M(-1) were determined.     

Self-assembly in two-dimensions of colloidal particles at liquid mixtures

The aim of this work is to simulate the formation of colloidal rings, circular clusters, and voids induced by oily lenses at the air-water interface. The presence of two liquids with different surface tension leads to the formation of a nonhomogeneous interface. In this case, the total interaction potential is assumed to be composed of only two terms; the first one is due to the (repulsive) pairwise dipolar force between partly immersed charged microspheres, whereas the second depends on the position of the particle at the interface and is connected to the interfacial stress caused by the difference of surface tension between both liquids. This simple potential is able to reproduce the experimental rings, circular clusters and voids found by different authors.     

A straightforward synthesis and structure of unprecedented iminium salts of dihydropyrido[3,2-e][1,3]thiazines

Unprecedented 2-iminium chloride salts of 5,8-dihydro-2H-pyrido[3,2-e][1,3]thiazines derivatives (8) were easily synthesized in one step from the corresponding o-chloroformyl-1,4-dihydropyridine (2) and thiourea. The structural study has been carried out by X-ray crystallography and theoretical calculations at the B3LYP/6-31G* levels and reveal that the new salts exhibit appropriate structural features to behave as calcium channel modulators.     

Calculation of CLD Using Population Balance Equations of Generating Functions: Linear and Non‐Linear Ideal Controlled Radical Polymerization

Population balance equations in terms of generating functions (GF) are used to predict chain length distributions (CLD) of linear and non‐linear ideal controlled radical polymerization (CRP) systems. It is here shown that under simplified conditions analytical solutions for the CLD can be found and moreover the fundamental CLD derived by H. Tobita in 2006 is a limiting case of the more general solutions here presented. In order to deal with more complex CRP systems, solutions based upon the numerical inversion of GF are presented. These studies are also extended to the non‐linear CRP of vinyl/divinyl monomers where multimodal CLDs are predicted to occur.

     

Molecular Architecture of Non-Linear Polymers: Kinetic Modeling and Experimental Characterization of the System Methyl Methacrylate + Ethylene Glycol Dimethacrylate

A general kinetic approach allowing the prediction of the molecular architecture of non-linear polymers is applied to the study of the copolymerization of methyl methacrylate (MMA) with ethylene glycol dimethacrylate (EGDMA). Dynamic predictions of molecular weight distributions, sequence length distributions and mean square radius of gyration are possible before and after gelation. A set of experiments concerning the copolymerization of MMA and EGDMA was carried out in toluene solution at 60 °C for which classic radical kinetics is a good approximation. The time evolution of key polymer properties was followed using a SEC system with a refractive index detector coupled with MALLS allowing the determination of absolute weight average molecular weight and apparent molecular size distributions as well as z-average radius of gyration. Special focus was given to assess the influence of the initial amount of cross-linker on the dynamics of the non-linear structure build-up of these products. A kinetic scheme comprising 23 different chemical species and 76 chemical reactions was used in the modeling studies of this chemical system. Most of the kinetic parameters used in the simulations have been collected from previous studies. For experiments at low monomer conversion (up to about 0.5) a good agreement between predictions and experimental measurements is observed for molecular weights and z-average radius of gyration by fitting a small number of parameters describing gel effect (with a conversion dependent but chain length independent termination rate parameter) and the relative propagation on pendant double bonds. However, predicted values of weight-average molecular weights and z-average radius of gyration before gelation are too low at higher monomer conversions with non-linear systems. The likely cause is the presence of intramolecular reactions which should not be neglected in these circumstances.     

A controller for 2-DOF underactuated mechanical systems with discontinuous friction

We propose a controller for a class of 2-DOF underactuated mechanical systems with discontinuous friction in the unactuated joint. The control objective is the regulation of the unactuated variable while the position and speed of the actuated joint remain bounded. The unactuated joint is considered as a mechanical system with discontinuous friction but continuous, artificial control input given by a term depending on the actuated positions and velocities. The proposed controller guarantees the convergence of the position error of the unactuated joint to zero, and it is robust with respect to some uncertainty in the discontinuous friction coefficients. We illustrate the technique with its application to two systems.     

Fluorinated resveratrol and pterostilbene

A general method for the synthesis of polyhydroxylated stilbene monofluorinated on the central double bond based on the Suzuki reaction between a bromofluoroolefin and a phenylboronic acid is described. Synthesis of fluorinated analogues of resveratrol and pterostilbene was achieved using this strategy.     

Standing waves for the NLS on the double-bridge graph and a rational–irrational dichotomy

We study standing waves of NLS equation posed on the double-bridge graph: two semi-infinite half-lines attached at a circle. At the two vertices Kirchhoff boundary conditions are imposed. The configuration of the graph is characterized by two lengths, $L_1$ and $L_2$. We study the solutions with possibly nontrivial components on the half-lines and a cnoidal component on the circle. The problem is equivalent to a nonlinear boundary value problem in which the boundary condition depends on the spectral parameter ω. After classifying the solutions with rational $L_1/L_2$, we turn to $L_1/L_2$ irrational showing that there exist standing waves only in correspondence to a countable set of negative frequencies ${\omega }_n$. Moreover we show that the frequency sequence admits cluster points and any negative real number can be a limit point of frequencies choosing a suitable irrational geometry $L_1/L_2$. These results depend on basic properties of diophantine approximation of real numbers.