A heterogeneous Bertrand duopoly game with bounded rational and adaptive players manufacturing differentiated products is subject of investigation. The main goal is to demonstrate that participation of one bounded rational player in the game suffices to destabilize the duopoly. The game is modelled with a system of two difference equations. Evolution of prices over time is obtained by iteration of a two dimensional nonlinear map. Equilibria are found and local stability properties thereof are analyzed. Complex behavior of the system is examined by means of numerical simulations. Region of stability of the Nash equilibrium is demonstrated in the plane of the speeds of adjustment. Period doubling route to chaos is presented on the bifurcation diagrams and on the largest Lyapunov characteristic exponent graph. Lyapunov time is calculated. Chaotic attractors are depicted and their fractal dimensions are computed. Sensitive dependence on initial conditions is evidenced.

Numerical values of the NRTL equation parameters for calculation of the vapour - liquid - liquid equilibria (VLLE) at atmospheric pressures have been presented for 5 ternary mixtures. These values were fitted to the experimental VLLE and vapour - liquid equilibrium (VLE) data to describe simultaneously, as accurately as possible, the VLE and the liquid - liquid equilibria (LLE). The coefficients of this model called further NRTL-VLL were used for simulations of n-propanol dehydration via heterogeneous azeotropic distillation. The calculations performed by a ChemCAD simulator were done for 4 mixtures using hydrocarbons, ether and ester as an entrainer. In majority simulations the top streams of the azeotropic column had composition and temperature similar to the corresponding experimental values of ternary azeotropes. The agreement between the concentrations of both liquid phases formed in a decanter and the experimental values of the LLE was good for all four simulations. The energy requirements were the most advantageous for the simulation with di-npropyl ether (DNPE) and isooctane. Simulations were performed also for one mixture using the NRTL equation coefficients taken from the ChemCAD database. In that case the compositions of the liquid organic phases leaving the decanter differed significantly from the experimental LLE data.

Heat flow in heterogeneous media with complex microstructure follows tortuous path and therefore determination of temperature distribution in them is a challenging task. Two-scales, micro-macro model of heat conduction with phase change in such media was considered in the paper. A relation between temperature distribution on the microscopic level, i.e., on the level of details of microstructure, and the temperature distribution on the macroscopic level, i.e., on the level where the properties were homogenized and treated as effective, was derived. The expansion applied to this relation allowed to obtain its more simplified, approximate form corresponding to separation of micro- and macro-scales. Then the validity of this model was checked by performing calculations for 2D microstructure of a composite made of two constituents. The range of application of the proposed micro-macro model was considered in transient states of heat conduction both for the case when the phase change in the material is present and when it is absent. Variation of the effective thermal conductivity with time was considered and a criterion was found for which application of the considered model is justified.

The paper presents current reports on kinetics and mechanisms of reactions with mercury which take place in the exhaust gases, discharged from the processes of combustion of solid fuels (coals). The three main stages were considered. The first one, when thermal decomposition of Hg components takes place together with formation of elemental mercury (Hg0). The second one with homogeneous oxidation of Hg0 to Hg2+ by other active components of exhaust gases (e.g. HCl). The third one with heterogeneous reactions of gaseous mercury (the both - elemental and oxidised Hg) and solid particles of fl y ash, leading to generation of particulate-bound mercury (Hgp). Influence of exhaust components and their concentrations, temperature and retention time on the efficiency of mercury oxidation was determined. The issues concerning physical (gas-solid) and chemical speciation of mercury (fractionation Hg0-Hg2+) as well as factors which have influence on the mercury speciation in exhaust gases are discussed in detail.

Distillation boundaries originate from saddle azeotropes, dividing the composition space into distillation regions. In heterogeneous mixtures distilled in packed columns, distillation regions overlap. The common area of distillation regions is parametrically sensitive, and it determines the possibilities of crossing (at a finite reflux) the distillation boundaries defined for a total reflux or reboil ratio. This work is an extended research of the paper (Królikowski et al., 2011) conducted to scrutinize whether the distillation regions overlapped in heteroazeotropic systems distilled in staged columns. Presented studies were performed by finding such composition points of the products, for which the rectifying profiles of staged columns were ended in different distillation regions. Calculations were executed for the heterogeneous mixture classified under Serafimov's topological class as 3.1-2: ethanol - benzene - water. Distillation regions for staged columns were found to overlap each other in the heterogeneous systems. As a result, their common part was parametrically sensitive.

Usually, cellular networks are modeled by placing each tier (e.g macro, pico and relay nodes) deterministically on a grid. When calculating the metric performances such as coverage probability, these networks are idealized for not considering the interference. Overcoming such limitation by realistic models is much appreciated. This paper considered two- tier twohop cellular network, each tier is consisting of two-hop relay transmission, relay nodes are relaying the message to the users that are in the cell edge. In addition, the locations of the relays, base stations (BSs), and users nodes are modeled as a point process on the plane to study the two hop downlink performance. Then, we obtain a tractable model for the k-coverage probability for the heterogeneous network consisting of the two-tier network. Stochastic geometry and point process theory have deployed to investigate the proposed two-hop scheme. The obtained results demonstrate the effectiveness and analytical tractability to study the heterogeneous performance.

A simple empirical study on the orientation, diameter, and extent of radial fractures (long and short) at the vicinity of the face-perpendicular preconditioned boreholes is described. Homogenous and heterogeneous mining faces were considered when studying the orientation of radial fractures, four and five face-perpendicular preconditioning practices were used to investigate the outspread and diameter of radial fractures from one blasted drill hole to another. Long radial fractures were observed to be developed along the direction of the maximum principal stress and short radial fractures were observed to be developed along the direction of the intermediate principal stress in a homogenous mining face. On the other hand, long radial fractures were observed to be developed along the direction of the intermediate principal stress, while short radial fractures were observed to be developed along the direction of the maximum principal stress when the mining faces subjected to heterogeneous rock mass. The diameters of the radial fractures observed were inconsistent and were not nine times the diameter of the original borehole. Furthermore, the extent of radial fractures from one borehole to another was noted to be gradually improved when the additional of preconditioned borehole was in place. This study maintained that the orientation of radial fractures is mostly controlled by the rock properties, however, extend and the diameters of the radial fractures are controlled by rock properties, the effectiveness of the stress wave and gas pressure and brittleness of the rock mass.

In the present paper, we investigate a multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.

In this work, a design equation was presented for a batch-recirculated photoreactor composed of a packed bed reactor (PBR) with immobilised TiO2-P25 nanoparticle thin films on glass beads, and a continuous-flow stirred tank (CFST). The photoreactor was studied in order to remove C.I. Acid Orange 7 (AO7), a monoazo anionic dye from textile industry, by means of UV/TiO2 process. The effect of different operational parameters such as the initial concentration of contaminant, the volume of solution in CFST, the volumetric flow rate of liquid, and the power of light source in the removal efficiency were examined. A rate equation for the removal of AO7 is obtained by mathematical kinetic modelling. The results of reaction kinetic analysis indicate the conformity of removal kinetics with Langmuir-Hinshelwood model (kL-H = 0.74 mg L-1 min-1, Kads = 0.081 mg-1 L). The represented design equation obtained from mathematical kinetic modelling can properly predict the removal rate constant of the contaminant under different operational conditions (R2 = 0.963). Thus the calculated and experimental results are in good agreement with each other.