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.

The paper considers a digital design of time-invariant systems in the case of step-invariant (ZOH), bilinear (Tustin's) and fractional order hold (FROH) discretization methods. The design problem is formulated as linear matrix inequalities (LMI). A closed-loop stability of the digitally designed control systems is discussed.

The study presents a mathematical model of the crystallisation of nodular graphite cast iron. The proposed model is based on micro- and macromodels, in which heat flow is analysed at the macro level, while micro level is used for modelling of the diffusion of elements. The use of elementary diffusion field in the shape of an averaged Voronoi polyhedron [AVP] was proposed. To determine the geometry of the averaged Voronoi polyhedron, Kolmogorov statistical theory of crystallisation was applied. The principles of a differential mathematical formulation of this problem were discussed. Application of AVP geometry allows taking into account the reduced volume fraction of the peripheral areas of equiaxial grains by random contacts between adjacent grains. As a result of the simulation, the cooling curves were plotted, and the movement of "graphite-austenite" and "austenite-liquid” phase boundaries was examined. Data on the microsegregation of carbon in the cross-section of an austenite layer in eutectic grains were obtained. Calculations were performed for different particle densities and different wall thicknesses. The calculation results were compared with experimental data.

A data warehouse (DW) is a large centralized database that stores data integrated from multiple, usually heterogeneous external

data sources (EDSs). DW content is processed by so called On-Line Analytical Processing applications, that analyze business trends, discover anomalies and hidden dependencies between data. These applications are part of decision support systems. EDSs constantly change their content and often change their structures. These changes have to be propagated into a DW, causing its evolution. The propagation of content changes is implemented by means of materialized views. Whereas the propagation of structural changes is mainly based on temporal extensions and schema evolution, that limits the application of these techniques. Our approach to handling the evolution of a DW is based on schema and data versioning. This mechanism is the core of, so called, a multiversion data warehouse. A multiversion DW is composed of the set of its versions. A single DWversion is in turn composed of a schema version and the set of data described by this schema version. Every DW version stores a DW state which is valid within a certain time period. In this paper we present: (1) a formal model of a multiversion data warehouse, (2) the set of operators with their formal semantics that support a DW evolution, (3) the impact analysis of the operators on DW data and user analytical queries. The presented formal model was a basis for implementing a multiversion DW prototype system.

A simple robust cheap LQG control is considered for discrete-time systems with constant input delay. It is well known that the full loop transfer recovery (LTR) effect measured by error function ∆(z) can only be obtained for minimum-phase (MPH) systems without time-delay. Explicit analytical expressions for ∆(z) versus delay d are derived for both MPH and NMPH (nonminimum-phase) systems. Obviously, introducing delay deteriorates the LTR effect. In this context the ARMAX system as a simple example of noise-correlated system is examined. The robustness of LQG/LTR control is analyzed and compared with state prediction control whose robust stability is formulated via LMI. Also, the robustness with respect to uncertain time-delay is considered including the control systems which are unstable in open-loop. An analysis of LQG/LTR problem for noise-correlated systems, particularly for ARMAX system, is included and the case of proper systems is analyzed. Computer simulations of second-order systems with constant time-delay are given to illustrate the performance and recovery error for considered systems and controllers.