Boundary layer in compressible flow of wet water vapour

In this paper the influence of small droplets, with radius $\text{10}{}^{\mathrm{?8}}\text{m}\text{< r < 10}{}^{\mathrm{?6}}\text{m}$, on laminar and turbulent boundary layer behavior is considered. It is found that the laminar boundary layer in a two-phase flow with strongly dispersed liquid retains dissipation energy and that the recovery factor of enthalpy is greater than unity. In turbulent boundary layers small droplets are transported by turbulent diffusion and this leads to the recovery factor being less than unity. Its value in both cases depends mainly on the nondimensional number $\text{Ds}\text{= C}{}_{\mathrm{Le}}\text{L/(U}{}_{\mathrm{e}}{}^2\text{/2)}$. The laminar boundary layer solution for non-equilibrium two-phase flow is obtained. Profiles of the droplet mass fraction, vapour and droplets temperatures and droplet radius are computed for the case of a steady two-dimensional flow. The turbulent boundary layer is treated using a semi-empirical theory assuming thermodynamic equilibrium.     

Perfect folk theorems. Does public randomization matter?

I consider two player games, where player 1 can use only pure strategies, and player 2 can use mixed strategies. I indicate a class of such games with the property that under public randomization both the discounted and the undiscounted finitely repeated perfect folk theorems do hold, but the discounted theorem does not without public randomization. Further, I show that the class contains games such that without public randomization the un-discounted theorem does not hold, as well as games such that without public randomization the undiscounted theorem does hold.I am grateful to Gita Gopinath for her close critical reading of an earlier version of the paper. I would like to acknowledge two anonymous referees for their detailed reports and suggestions. Financial support from the Foundation for Polish Science is also gratefully acknowledged.     

Indirect coulometric determination of platinum based on the ascorbic acid—iodine system

Platinum(IV) can be determined by addition of an excess of ascorbic acid solution and back-titration with anodically generated iodine to a biamperometric end-point. Conditions have been established for quantitative reduction of platinum(IV) and elimination of oxidation of piatinum(II) by the generated iodine. The determination is carried out at pH 5, and the accuracy and precision are better than 0.5% for platinum in the range 5–20 nag.     

Fixed-point index for compositions of set-valued maps with proximally ∞-connected values on arbitrary ANR's

In the paper the integer-valued fixed-point index theory for compositions of set-valued maps having proximally ∞-connected values satisfying all the axioms of a fixed point index is presented. The considered approach is based on the technique of single-valued approximation on the graph.     

Convective stability of hot matter in ultrarelativistic heavy-ion collisions

The convective stability of strongly interacting matter undergoing hydrodynamic flow in ultrarelativistic heavy-ion collisions is studied in both the quark-gluon plasma and hadron gas phases. We find that this stability depends on the form of the initial conditions assumed for the hydrodynamic flow. In the case of initial conditions corresponding to partial transparency the flow of the quark-gluon plasma is stable whereas the flow of the hadron gas is convectively unstable. The timescale for hydrodynamic oscillations around the (stable or unstable) equilibrium state is found to be larger than the expected lifetime of the system, suggesting that the flow in either case is close to neutral convective equilibrium.     

The mass spectrometric fragmentation of some diastereoisomeric 4-methyl-1,3,2-dioxaphosphorinanes

The mass spectra of nine diastereoisomeric pairs of 4-methyl-2-X-2-Y-1,3,2-dioxaphosphorinanes have been examined. The differences between the intensities of particular ions in the mass spectra of geometrical isomers are reported and rationalized in terms of the conformations adopted by compounds.     

The reaction of optically active α-aminocarboxylic acid hydrazides with triethyl orthoesters

New derivatives of 2-(1-amino-1-phenylmethyl)-1,3,4-oxadiazole and 1,2,4-triazin-6-one were synthesised in the reactions of optically active α-aminocarboxylic acid hydrazides and triethyl orthoesters in xylene. The electronic and steric effects of substituents at the α position influencing the formation of five- or six-membered products are discussed.     

How does mechanism of biosorption determine the differences between the initial and equilibrium adsorption states?

The analysis of various models assumed to represent the influence of pH on heavy metals biosorption equilibrium is presented. It shows that all of them lead to the same mathematical expressions (e.g. the Langmuir or the Flory adsorption isotherm equations) when the pH effects are neglected. Even if considering the pH effects, some of them (competitive adsorption and ion-exchange models, for instance) still lead to analogical expressions for sorption isotherm equations. The accepted mechanism of biosorption may, however, influence strongly the differences between the initial and equilibrium states of biosorption system.