On ergodic control of degenerate diffusions

For the ergodic control problem with degenerate diffusions, the existence of an optimal solution is established for various interesting classes of solutions.This research was supported by Grant No. 26/01/92-G from the Department of Atomic Energy, Government of India, Delhi, India.     

A remark on control of partially observed Markov chains

A new state variable is introduced for the problem of controlling a Markov chain under partial observations, which, under a suitably altered probability measure, has a simple evolution.     

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.     

Erratum to: Risk-Sensitive Control with Near Monotone Cost

The infinite horizon risk-sensitive control problem for non-degenerate controlled diffusions is analyzed under a ‘near monotonicity’ condition on the running cost that penalizes large excursions of the process.     

Ergodic Control of Partially Degenerate Diffusions in a Compact Domain

The problem of ergodic control of a reflecting diffusion in a compact domain is analysed under the condition of partial degeneracy, i.e. when its transition kernel after some time is absolutely continuous with respect to the Lebesgue measure on a part of the state space. Existence of a value function and a “martingale dynamic programming principle” are established by mapping the problem to a discrete time control problem. Implications for existence of optimal controls are derived.     

Study of Forced Degradation Behaviour of Brinzolamide Using LC–ESI–Q-TOF and In Silico Toxicity Prediction

Brinzolamide (BZA) is a topical ophthalmic drug which is generally used to lower the intraocular pressure during glaucoma. It was subjected to forced degradation studies under hydrolytic (acidic, basic), oxidative, photolytic and thermal stress conditions; the drug degraded significantly in hydrolytic and oxidative conditions, leading to the formation of seven degradation products in total. It was stable on exposure to light and dry heat in the solid state. An ultra-performance liquid chromatography (UPLC) method was developed on a Waters CSH phenyl hexyl column (100 × 2.1 mm, 1.7 µm), using gradient elution of 0.1 % formic acid and methanol as mobile phase. The method was extended to quadrupole time-of-flight mass spectrometry (Q-TOF–MS) for the structural characterisation. All degradation products were comprehensively characterised by UHPLC–ESI/MS/MS experiments. The most probable mechanisms for the formation of degradation products were also proposed. In silico toxicity of the drug and its degradation products was determined using TOPKAT toxicity prediction software.

     

Direct equilibration of soil water for delta(18)O analysis and its application to tracer studies

Current methods for stable oxygen isotopic (delta (18)O) analysis of soil water rely on separation of water from the soil matrix before analysis. These separation procedures are not only time consuming and require relatively large samples of soil, but also have been shown to introduce a large potential source of error. Current research at Queen's University Belfast is focused on using direct equilibration of CO(2) with the pore water to eliminate this extraction step using the automated Multiprep system and a Micromass Prism III isotope ratio mass spectrometer (IRMS). The findings of this research indicate the method is less time consuming, more reliable, and reproducible to within accepted limits (+/-0.1% per thousand delta (18)O). In this study the direct equilibration method is used to analyse delta (18)O tracer profiles in the unsaturated zone of field soils, concurrently with chloride tracer profiles, which can be used to assess infiltration rates and mechanisms through the unsaturated zone. Copyright 1999 John Wiley & Sons, Ltd.     

Secondary ion yields produced by keV atomic and polyatomic ion impacts on a self-assembled monolayer surface

A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd.     

The study of the changes in the thermal properties of <Emphasis Type="Italic">Labeo rohita</Emphasis> bones due to arsenic exposure

The paper presents the changes in the thermal properties of control, arsenic exposed and DMSA treated Labeo rohita bones by using thermo analytical techniques. The result shows that the mass loss due to the thermal decomposition occurs in three distinct steps due to loss of water, organic and inorganic materials. The arsenic exposed bones present a different thermal behaviour compared to the control bones. The residue masses are increased due to arsenic exposure, while the DMSA treatment reduces the residue mass level. These thermal characteristics can be used as a qualitative method to check the metal accumulation in samples.     

On the Hamiltonicity Gap 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 these policies. 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, ε, is sufficiently small, the minimum of this functional over the space of the doubly stochastic policies is attained at a Hamiltonian cycle, provided that the graph is Hamiltonian. We also show that when the graph is non‐Hamiltonian, the above minimum is strictly greater than that in a Hamiltonian case. We call the size of this difference the “Hamiltonicity Gap” and derive a conservative lower bound for this gap. Our results imply that the Hamiltonian cycle problem is equivalent to the problem of minimizing the variance of the first hitting time of the home node, over doubly stochastic policies. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009