The tightness in the ergodic analysis of regenerative queueing processes

The tightness of some queueing stochastic processes is proved and its role in an ergodic analysis is considered. It is proved that the residual service time process in an open Jackson-type network is tight. The same problem is solved for a closed network, where the basic discrete time process is embedded at the service completion epochs. An extention of Kiefer and Wolfowitz's “key” lemma to a nonhomogeneous multiserver queue with an arbitrary initial state is obtained. These results are applied to get the ergodic theorems for the basic regenerative network processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Distribution and reaction dynamics of iron(III) hydrolytic cationic species

Studying hydrolysis of iron(III) ions contained in the concentration 0.01 mol/L in the Fe³⁺-NO₃⁻H₂O system as a function of increasing pH, we determined the regions of the dominance of various complex species and their interconversions. The reaction dynamics of transformations of various hydroxo complex species is represented.     

Stability of Jackson Type Network Output

We consider an open Jackson type queueing network N with input epochs sequence I={T _n ⁽⁰⁾,n0}, T ₀ ⁽⁰⁾=0, assume another input ={ _n ⁽⁰⁾} and denote _k =| _k ⁽⁰⁾–T _k ⁽⁰⁾|, ₀=0, _n =max_{1kn k} , n1. Let {T _n } and { _n } be the output points in network N and in modified network, with input , accordingly. We study the long-run stability of the network output, establishing two-sided bounds for output perturbation via input perturbation. In particular, we obtain conditions that imply max _kn |T _k – _k |=o(n ^1/r ) with probability 1 as n for some r>0. This result is also extended to continuous time. We consider successively separate station (service node), tandem and feedforward networks. Then we extend stability analysis to general (feedback) networks and show that in our setting these networks can be reduced to feedforward ones. Similar stability results are also obtained in terms of the number of departures. Application to a tandem network with the overloaded stations is considered.     

Distribution and dynamics of transformation of hydrolytic cationic forms of nickel(II)

A system Ni²⁺-NO₃⁻-H₂O was examined by dialysis under equilibrium conditions using step constants of hydrolysis to constructs distribution diagrams of Ni(II) cationic forms in a dependence on a pH value of a solution. We considered the reaction dynamics of hydrolytic cationic forms of nickel(II) and substantiated schemes of realized processes with a change in pH.     

Vibration Spectra of Coprecipitated Fe(III)-Ni(II) and Fe(III)-Cu(II) Hydroxides and of the Products of Their Thermolysis

A range of coprecipitated Fe(III)-Me(II) (Me(II) = Ni, Cu) hydroxides and of the products of their thermolysis have been investigated by the IR spectroscopy method. The basic absorption bands has been assigned, and the chemistry of the process of formation of coprecipitated hydroxides has been discussed from the standpoint of generation of heteronuclear hydrococomplexes.