Sequential Norrish Type II Photoelimination and Intramolecular Aldol Cyclization of α‐Diketones: Synthesis of Polyhydroxylated Cyclopentitols by Ring Contraction of Hexopyranose Carbohydrate Derivatives

The excitation of the innermost carbonyl of nono‐2,3‐diulose derivatives by irradiation with visible‐light initiates a sequential Norrish type II photoelimination and aldol cyclization process that finally gives polyfunctionalized cyclopentitols. The rearrangement has been confirmed by the isolation of stable acyclic photoenol intermediates that can be independently cyclized by a thermal 5‐(enolexo)‐exo‐trig uncatalyzed aldol reaction with high diastereoselectivity. In this last step, the large deuterium kinetic isotope effect found for the 1,5‐hydrogen atom transfer seems to indicate that the aldol reaction runs through a concerted pericyclic mechanism. Owing to the ready availability of pyranose sugars of various configurations, this protocol has been used to study the influence of pyranose ring‐substituents on the diastereoselectivity of the aldol cyclization reaction. In contrast with other pyranose ring contraction methodologies no transition‐metal reagents are needed and the sequential rearrangement occurs simply by using visible light and moderate heating (0 to 60 °C).     

Threshold policies for controlled retrial queues with heterogeneous servers

Retrial queues are an important stochastic model for many telecommunication systems. In order to construct competitive networks it is necessary to investigate ways for optimal control. This paper considers K -server retrial systems with arrivals governed by Neut' Markovian arrival process, and heterogeneous service time distributions of general phase-type. We show that the optimal policy which minimizes the number of customers in the system is of a threshold type with threshold levels depending on the states of the arrival and service processes. An algorithm for the numerical evaluation of an optimal control is proposed on the basis of Howar's iteration algorithm. Finally, some numerical results will be given in order to illustrate the system dynamics. AMS subject classification: 60K25 93E20     

On inductively minimal geometries that satisfy the intersection property

We prove that, up to isomorphism, for a given positive integer n, there is only one inductively minimal pair (Γ,Sym(n)) of rank n-1 that satisfies the intersection property. Moreover, we show that the diagram of Γ is linear.     

An atlas of regular thin geometries for small groups

For some small groups, we give, up to isomorphism, an exhaustive list of all residually connected thin geometries on which these groups act regularly. We then show the utility of such an atlas by proving several results about smallest groups acting on a given diagram. The results have been obtained using a series of MAGMA programs.

     

Semi-Automated Production Systems under Disturbances

A production system operates at a speed which is a stationary stochastic process. Given the routine control point, the actual accumulated production observed at that point and the deterministic rate of demand, the decision-maker determines the timing of the next control point. The problem is applied to semiautomated production processes where the advancement of the process cannot be measured or viewed continuously, and the process has to be controlled in discrete points by the decision-maker. Since the cost of performing a single control is relatively high, the control should be carried out as rarely as possible but it also has to ensure a preset confidence probability of achieving production output no less than that required. Formulae for determining the next control point for an arbitrary distribution function of the stationary process with a certain autocorrelation function are presented. They depend on the status of the system (shortage or surplus), the relation between the rate of demand and the mean value of the speed, the variance of the speed, and on the confidence level 1-α. A practical numerical example from the mining industry will be given.     

Numerical simulation of time‐dependent hydrodynamic removal of a contaminated fluid from a cavity

The time‐dependent hydrodynamic removal of a contaminated fluid from a rectangular cavity on the floor of a duct is analysed numerically. Laminar duct flows are considered for Reynolds numbers of 50 and 1600 where the characteristic length is the duct height. Two cases are considered where: (1) the fluid density in the cavity is the same as that for the duct fluid and (2) the cavity fluid has a higher density than the duct fluid but the two fluids are miscible. The flow is solved by a numerical solution of the time‐dependent Navier–Stokes equations. Attention is focused on the convective transport of contaminated fluid out from the cavity and the effect of duct flow velocity profile on the cleaning process. Passive markers are used in the numerical simulation for the purpose of identifying the contaminated cavity fluid. The results show that the flow patterns in the cavity are influenced by the type of duct flow. From a cleaning perspective, the results suggest that it is easier for the duct flow to penetrate a cavity and to remove contaminated cavity fluid when the duct flow is of the Poiseuille type and the aspect ratio is large. Copyright © 2003 John Wiley & Sons, Ltd.     

Investigation of chemically modified barium titanate beads as surface-enhanced Raman scattering (SERS) active substrates for the detection of benzene thiol, 1,2-benzene dithiol, and rhodamine 6G

SERS active surfaces were prepared by depositing silver films using Tollen's reaction on to barium titanate beads. The SERS activity of the resulting surfaces was probed using two thiols (benzene thiol and 1,2-benzene dithiol) and rhodamine 6G. The intensity of the SERS signal for the three analytes was investigated as a function of silver deposition time. The results indicate that the SERS intensity increased with increasing thickness of the silver film until a maximum signal intensity was achieved; additional silver deposition resulted in a decrease in the SERS intensity for all of the studied molecules. SEM measurement of the Ag coated barium titanate beads, as a function of silver deposition time, indicate that maximum SERS intensity corresponded with the formation of atomic scale islands of silver nanoparticles. Complete silver coverage of the beads resulted in a decreased SERS signal and the most intense SERS signals were observed at deposition times of 30 min for the thiols and 20 min for rhodamine 6G.