On extremal solutions to stochastic control problems

We identify two solutions of a controlled diffusion if the corresponding one-dimensional marginals of the state and control process agree. The extreme points of the set of such equivalence classes are shown to correspond to Markov controls.     

On the Milito-Cruz adaptive control scheme for Markov chains

Milito and Cruz have introduced a novel adaptive control scheme for finite Markov chains when a finite parametrized family of possible transition matrices is available. The scheme involves the minimization of a composite functional of the observed history of the process incorporating both control and estimation aspects. We prove the a.s. optimality of a similar scheme when the state space is countable and the parameter space a compact subset ofR ^d .     

Chemical synthesis, characterization and transport properties of copolymer: Poly(aniline-co-m-methylaniline)

Poly(aniline-co-m-methylaniline) were copolymerized by chemical peroxidation of aniline and m-methylaniline in aqueous acidic medium under nitrogen atmosphere at 0–4oC. The molar feed ratio of the monomers were varied to prepare copolymers of different composition. The copolymers product were characterized by solubility, spectroscopic methods, elemental analysis and electrical conductivity measurements. The solubility and spectroscopic analysis suggested that the product is a copolymer of aniline and m-methylaniline. The optical spectra of the copolymer shows hypsochromic shift with the increase in dielectric constant of the solvent and with increasing the content of m-methylaniline in the copolymer chain. The electrical conductivity of copolymer salts were measured as a function of temperature. The conductivity of copolymer decreases with increasing the content of m-methylaniline in the copolymer chain, due to change in coplanarity of polymer and reduction of mobility of charge carrier along the main chain. The conduction mechanism of copolymer is polaron hopping conduction as similar to the case of polyaniline. The coherence, most probable hopping distance, hopping energy and localization length of copolymers have been compared to those of homopolymers.     

Temperatures and kinetics of anatase to rutile transformation in doped TiO<Subscript>2</Subscript> heated in microwave field

The influence of aliovalent ions such as Mn, Cr, Fe, Mo, and V on the temperature and kinetics of anatase to rutile phase transformation in TiO₂ heated in microwave field was studied in this work. The results indicated that heat treatment method and dopants considerably affected the anatase-to-rutile phase transition temperature and kinetics of transformation. The activation energy for anatase to rutile transformation of TiO₂ derived from the isothermal data was found to be 328.4 kJ mol^–1, which was considerably reduced by the addition of dopants in TiO₂ matrix. The activation energy for Mo, Mn and V doped samples was 252.0, 101.3 and 96.4 kJ mol^–1, respectively.     

Perspective on metal-mediated polar monomer/alkene copolymerization

A major unsolved problem in polymer synthesis is the design of efficient metal-mediated systems for the copolymerization of alkenes with polar vinyl monomers, such as acrylates and methacrylates. There are several reasons for the absence of efficient transition metal-based insertion copolymerization catalysts. First, following insertion, the ester group of the acrylate coordinates to the metal thereby hindering subsequent monomer coordination. A second reason stems from the preferred 2,1-insertion of acrylates into metal-carbon bonds resulting in the placement of the ester group on the α-carbon. This makes the metal-alkyl species particularly prone to homolysis because of the enhanced stability of the resultant alkyl radical, one that is essentially the same as the propagating species in radical-initiated acrylate polymerization. In this perspective we focus on this issue of facile metal-carbon bond homolysis, especially following acrylate insertion, using examples from our own work. We suggest ways to circumvent these issues, for example forcing 1,2-insertion by imposing steric crowding at the metal. Finally, we discuss the danger of relying on radical traps as probes for polymerization mechanism. Radical traps can react with metal-hydrides and attenuate metal-centered nonradical reactions. However, even when radical traps fail to stop an observed polymerization, it may be wrong to conclude that a nonradical mechanism is at work since the traps can be destroyed under certain reaction conditions.     

On the spin coating of viscoplastic fluids

The spin coating of a viscoplastic material is studied using a continuous viscosity function. Thus, the transient model requires the calculation of only velocity, pressure and the moving-free surface of the liquid film, but not the calculation of the yield surface within the liquid. A Finite Element/Newton-Raphson method is presented for solving this moving boundary problem after mapping the deforming domain onto a fixed one. Assuming axial symmetry, the effect of the Bingham, Reynolds, Capillary and gravitational Bond numbers is examined. The magnitude of the first two parameters affects significantly the flow field and the shape of the film as well as the required spinning time in order to produce a film of uniform thickness. Depending on their values, large departures from the corresponding Newtonian solution may be obtained. In these cases the film does not thin out uniformly, but a maximum in its profile is created at the center of the disk. Then, the magnitude of the Capillary number also affects the size of this maximum. The gravitational Bond number affects the film thickness and its profile to a lesser extent.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Directed graphs,Hamiltonicity and doubly stochastic matrices

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)‐entry of the fundamental matrices of the Markov chains induced by the same policies. In particular, we focus on the subset of these policies that induce doubly stochastic probability transition matrices, which we refer to as the “doubly stochastic policies.” We show that when the perturbation parameter ? is sufficiently small the minimum of this functional over the space of the doubly stochastic policies is attained very close to a Hamiltonian cycle, provided that the graph is Hamiltonian. We also derive precise analytical expressions for the elements of the fundamental matrix that lend themselves to probabilistic interpretation as well as asymptotic expressions for the first diagonal element, for a variety of deterministic policies that are of special interest, including those that correspond to Hamiltonian cycles. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Identification and characterization of stressed degradation products of metoprolol using LC/Q-TOF-ESI-MS/MS and MS(n) experiments

A rapid, specific and reliable isocratic high-performance liquid chromatography combined with quadrupole time-of-flight electrospray ionization tandem mass spectrometry (LC/Q-TOF-ESI-MS/MS) method has been developed and validated for the identification and characterization of stressed degradation products of metoprolol. Metoprolol, an anti-hypertensive drug, was subjected to hydrolysis (acidic, alkaline and neutral), oxidation, photolysis and thermal stress, as per ICH-specified conditions. The drug showed extensive degradation under oxidative and hydrolysis (acid and base) stress conditions. However, it was stable to thermal, neutral and photolysis stress conditions. A total of 14 degradation products were observed and the chromatographic separation of the drug and its degradation products was achieved on a C(18) column (4.6 × 250 mm, 5 μm). To characterize degradation products, initially the mass spectral fragmentation pathway of the drug was established with the help of MS/MS, MS(n) and accurate mass measurements. Similarly, fragmentation pattern and accurate masses of the degradation products were established by subjecting them to LC-MS/QTOF analysis. Structure elucidation of degradation products was achieved by comparing their fragmentation pattern with that of the drug. The degradation products DP(2) (m/z 153) and DP(14) (m/z 236) were matched with impurity B, listed in European Pharmacopoeia and British Pharmacopoeia, and impurity I, respectively. The LC-MS method was validated with respect to specificity, linearity, accuracy and precision.     

Unprecedented synergistic effects between weak Lewis and Brønsted acids in Prins cyclization

Novel synergistic effects between Lewis and Br?nsted acids in Prins cyclization are reported. Non-reactive Lewis acids and non-reactive Br?nsted acids, which failed to perform Prins cyclization when used alone, have shown remarkable synergistic effects when used in combination to perform the reaction successfully.