Convex duality and the Skorokhod Problem. II

In this paper we consider Skorokhod Problems on polyhedral domains with a constant and possibly oblique constraint direction specified on each face of the domain, and with a corresponding cone of constraint directions at the intersection of faces. In part one of this paper we used convex duality to develop new methods for the construction of solutions to such Skorokhod Problems, and for proving Lipschitz continuity of the associated Skorokhod Maps. The main alternative approach to Skorokhod Problems of this type is the reflection mapping technique introduced by Harrison and Reiman [8]. In this part of the paper we apply the theory developed in part one to show that the reflection mapping technique of [8] is restricted to a slight generalization of the class of problems originally considered in [8]. We further illustrate the power of the duality approach by applying it to two other classes of Skorokhod Problems – those with normal directions of constraint, and a new class that arises from a model of processor sharing in communication networks. In particular, we prove existence of solutions to and Lipschitz continuity of the Skorokhod Maps associated with each of these Skorokhod Problems. Received: 17 April 1998 / Revised: 8 January 1999     

Bounds on Lifting Continuous-State Markov Chains to Speed Up Mixing

It is often possible to speed up the mixing of a Markov chain \(\{ X_{t} \}_{t \in \mathbb {N}}\) on a state space \(\Omega \) by lifting, that is, running a more efficient Markov chain \(\{ \widehat{X}_{t} \}_{t \in \mathbb {N}}\) on a larger state space \(\hat{\Omega } \supset \Omega \) that projects to \(\{ X_{t} \}_{t \in \mathbb {N}}\) in a certain sense. Chen et al. (Proceedings of the 31st annual ACM symposium on theory of computing. ACM, 1999) prove that for Markov chains on finite state spaces, the mixing time of any lift of a Markov chain is at least the square root of the mixing time of the original chain, up to a factor that depends on the stationary measure of \(\{X_t\}_{t \in \mathbb {N}}\). Unfortunately, this extra factor makes the bound in Chen et al. (1999) very loose for Markov chains on large state spaces and useless for Markov chains on continuous state spaces. In this paper, we develop an extension of the evolving set method that allows us to refine this extra factor and find bounds for Markov chains on continuous state spaces that are analogous to the bounds in Chen et al. (1999). These bounds also allow us to improve on the bounds in Chen et al. (1999) for some chains on finite state spaces.     

GC�CMS Coupled with Hollow-Fiber Drop-to-Drop Solvent Microextraction for Determination of Antidepressants Drugs in Human Blood Sample

A simple, rapid and sensitive hollow-fiber with drop-to-drop solvent microextraction (HF-DDSME) combined with gas chromatography?Cmass spectrometry (GC?CMS) has been successfully developed for extraction and determination of antidepressants drugs (AD) in blood sample. The parameters that affect the separation and preconcentration of AD from sample solution were investigated. Calibration curve obtained for three AD were in the range of 100?C1,000; 150?C1,200; and 80?C1,200 ng mL^?1 for amitriptyline, imipramine, and promethazine, respectively, with correlation coefficient (R ² ) between 0.990 and 0.997. The limit of detection (LOD) obtained for amitriptyline, imipramine and promethazine was 25, 30 and 18 ng mL^?1, respectively. The developed method has been successfully applied for the determination of AD concentration in blood sample, and the recoveries for the spiked samples were in the range of 92.3?C97.6%. The sample preparation procedure is very simple, effective and virtually solvent-free, and indicated to be a good alternative for the traditional liquid?Cliquid extraction. Finally, the proposed method was successfully applied for the determination of drug concentration of AD in human blood sample.     

Synthesis for Pyridopyrimidinones

An improved clean methodology has been developed for the synthesis of pyrido[2,3‐d]pyrimidin‐4‐ones through a simple one‐pot reaction of chalcones, ketones, and ammonium acetates via a [3+2+1] ring annulation. This dry media methodology, where the three components absorbed over solid inorganic support under microwave irradiation, afforded the desired product in a short reaction time.     

Stability of gold cages (Au<Subscript>16</Subscript> and Au<Subscript>17</Subscript>) at finite temperature

We have employed ab initio molecular dynamics to investigate the stability of the smallest gold cages, namely Au₁₆ and Au₁₇, at finite temperatures. First, we obtain the ground state structure along with at least 50 distinct isomers for both the clusters. This is followed by the finite temperature simulations of these clusters. Each cluster is maintained at 12 different temperatures for a time period of at least 150 ps. Thus, the total simulation time is of the order of 2.4 ns for each cluster. We observe that the cages are stable at least up to 850 K. Although both clusters melt around the same temperature, i.e. around 900 K, Au₁₇ shows a peak in the heat capacity curve in contrast to the broad peak seen for Au₁₆.