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.     

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.     

Denumerable controlled Markov chains with strong average optimality criterion: Bounded & unbounded costs

This paper studies discrete-time nonlinear controlled stochastic systems, modeled by controlled Markov chains (CMC) with denumerable state space and compact action space, and with an infinite planning horizon. Recently, there has been a renewed interest in CMC with a long-run, expected average cost (AC) optimality criterion. A classical approach to study average optimality consists in formulating the AC case as a limit of the discounted cost (DC) case, as the discount factor increases to 1, i.e., as the discounting effectvanishes. This approach has been rekindled in recent years, with the introduction by Sennott and others of conditions under which AC optimal stationary policies are shown to exist. However, AC optimality is a rather underselective criterion, which completely neglects the finite-time evolution of the controlled process. Our main interest in this paper is to study the relation between the notions of AC optimality andstrong average cost (SAC) optimality. The latter criterion is introduced to asses the performance of a policy over long but finite horizons, as well as in the long-run average sense. We show that for bounded one-stage cost functions, Sennott's conditions are sufficient to guarantee thatevery AC optimal policy is also SAC optimal. On the other hand, a detailed counterexample is given that shows that the latter result does not extend to the case of unbounded cost functions. In this counterexample, Sennott's conditions are verified and a policy is exhibited that is both average and Blackwell optimal and satisfies the average cost inequality.     

Access to the spiro hydrindandione ring system of Fredericamycin A through a Friedel-Crafts reaction.

Condensation of 1,4-dimethoxybenzene with 1,1-cyclopentane dicarboxylic acid or 1,1-indan dicarboxylic acid derivatives led to the title compounds.     

Equivalence of Lyapunov stability criteria in a class of Markov decision processes

We are concerned with Markov decision processes with countable state space and discrete-time parameter. The main structural restriction on the model is the following: under the action of any stationary policy the state space is acommunicating class. In this context, we prove the equivalence of ten stability/ergodicity conditions on the transition law of the model, which imply the existence of average optimal stationary policies for an arbitrary continuous and bounded reward function; these conditions include the Lyapunov function condition (LFC) introduced by A. Hordijk. As a consequence of our results, the LFC is proved to be equivalent to the following: under the action of any stationary policy the corresponding Markov chain has a unique invariant distribution which depends continuously on the stationary policy being used. A weak form of the latter condition was used by one of the authors to establish the existence of optimal stationary policies using an approach based on renewal theory.This research was supported in part by the Third World Academy of Sciences (TWAS) under Grant TWAS RG MP 898-152.     

Contractive Approximations in Risk-Sensitive Average Semi-Markov Decision Chains on a Finite State Space

Journal of Optimization Theory and Applications - This work concerns with semi-Markov decision chains evolving on a finite state space. The controller has a positive and constant risk sensitivity...     

The Photobiological Differences of Gilvocarcins V and M Are not Related to their Transient Intermediates and Triplet Yields

Abstract— The transient absorption spectra of the intermediates produced by the 355 nm laser excitation of gilvocarcin derivatives have been investigated in various solvents. The spectra consist of a triplet-triplet absorption in the visible region and a residual absorption observed between 340 and 700 nm due to a long-lived species, assigned to the radical cation. A broad-fast decaying band with a maximum at around 700 nm attributed to the solvated electron is also seen in solutions containing a low DMSO/water volume ratio and at 266 nm irradiation of a 50% methanol/water solvent mixture. The molar absorption coefficient of the triplet state of gilvocarcin V (GV) and gilvocarcin M (GM), determined by the energy transfer method, is independent of the solvent properties and has a value of 3.0 × 10⁴/ M cm. The triplet decay rate constants for both drugs are between 1 and 5 × 10⁴/s. A similar initial yield and triplet decay rate constant of GV were observed in the presence of 3.4 m M thymine. Thus, a quenching rate constant of the GV's triplet state by thymine is estimated to be lower than 10⁶/Ms. The triplet quantum yields of both antibiotics determined by using the comparative method are higher in dimethylsulfoxide (DMSO) (0.18) than are those corresponding to 25% DMSO/water (0.06). The decrease in φ_T in the presence of water could be attributed to an enhanced internal conversion rate constant from the S₁ state or to an increase in the photoionization yield. The similarity of the transient intermediates and their yields for GV and GM suggest that their photobiological differences are due to other factors such as DNA binding constants, preferential localization of the drugs in the cell or the enhanced reactivity of the vinyl group toward cellular components.