Chlorination of aromatic substrates catalyzed by the phthalocyanine complexes

The chlorination of benzene, toluene, and o-xylene with molecular chlorine in the presence of the phthalocyanine complexes of different structures was studied. The transformations of the catalysts during the reaction were investigated. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1644–1647, August, 2008.     

Influence of transition metal ions on the textural properties of alumina and aluminasilicates

Accelerated phase transformations and chemical reactions of metastable aluminas and kaolinite, doped with Cu^{2 +}, Mn^{3 +}/Mn^{2 +} and Fe^{3 +}/Fe^{2 +} ions, are accompanied with accelerated decrease of surface area and pore volume values. The phenomena in metal ion doped samples are explained by a catalytic mechanism, in terms of the Jahn-Teller effect. This revised version was published online in June 2006 with corrections to the Cover Date.     

Equivalence and Singularity of Gaussian Measures on the Conic Sigma-Field

The alternative: equivalence-singularity on the conic sigma-field is established for a pair of centered Gaussian distributions and a corresponding criterion is given. The behavior of the logarithmic variation is established for the Radon–Nikodym derivative on the conic sigma-subfield. Bibliography: 6 titles.     

Adaptive server staffing in the presence of time-varying arrivals: a feed-forward control approach

We study the short-term staffing problem of systems that experience random, non-stationary demand. The typical method to accommodate changes in arrival rate is to use historical data to identify peak periods and associated forecasting for upcoming time windows. In this paper, we develop a method that instead detects change as it happens. Motivated by an automatic call distributor system in a call centre with time-varying arrivals, we propose a change detection algorithm based upon non-homogeneous Poisson processes. The proposed method is general and may be thought of as a feed-forward strategy, in which we detect a change in the arrival process, estimate the new magnitude of the arrival rate, and assign an appropriate number of servers to the tasks. The generalized likelihood ratio statistic is used and a recommendation for its decision limit is developed. Simulation results are used to evaluate the performance of the detector in the context of a telephone call centre.     

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali–Hahn–Saks theorem are given.     

PERIODIC ENVIRONMENTS AND PERIODIC HARVESTING

ABSTRACT. We consider autonomous population models under periodic harvesting and population models in periodic environments and seek conditions under which there is an asymptotically stable periodic solution.