A standard solution regarding business process management automation in enterprises is the use of workflow management systems working by the Rule-Based Reasoning approach. In such systems, the process model which is designed entirely before the implementation has to meet all needs deriving from business activity of the organization. In practice, it means that great limitations arise in process control abilities, especially in the dynamic business environment. Therefore, new kinds of workflow systems may help which typically work in more agile way e.g. following the Case-Based Reasoning approach. The paper shows another possible solution – the use of emergence theory which indicates among other conditions required to fulfill stimulation of the system (for example the business environment) to run grass-roots processes that lead to arising of new more sophisticated organizing forms. The paper also points the using opportunity of such techniques as the processing of complex events to fulfill key conditions pointed by the emergence theory.

Appropriate business processes management (BPM) within an organization can help attain organizational goals. It is particularly important to effectively manage the lifecycle of these processes for organizational effectiveness in improving ever-growing performance and competitivity-building across the company. This paper presents a process discovery and how we can use it in a broader framework supporting self-organization in BPM. Process discovery is intrinsically associated with the process lifecycle. We have made a pre-evaluation of the usefulness of our facts using a generated log file. We also compared visualizations of the outcomes of our approach with different cases and showed performance characteristics of the cash loan sales process.

The approximation of a fractional order PIλDμ-controller transfer function using a chain fraction theory is considered. Analytical expressions for the approximation of s±α components of the transfer functions of PIλDμ-controllers were obtained through the application of the chain fraction theory. Graphs of transition functions and frequency characteristics of Dμ (α = μ = 0.5) and Iλ (α = λ = −0.5) parts for five different decomposition orders were obtained and analyzed. The results showed the possibility of applying the approximation of the PIλDμ-controller transfer function by the method of chain fractions with different valuesof λ and μ. For comparison, the transfer functions with the same order polynomials, obtained by the methods of Oustaloup transformation and chain fractions, were approximated for α = ±0.5. The analysis proved the advantages of using the chain fraction method to approximate the transfer function of the PIλDμ-controller. The performed approximation opens up the possibility of developing engineering methods for the technical implementation of PIλDμ-controllers. The accuracy of the same order transfer function approximation is higher when the method of chain fractions is used. It has been established that the adequacy of the frequency characteristics of the transfer functions obtained by the chain fraction method also depends on the approximation order.

Active resources concept of computation for enterprise software MACIEJ KORYL Traditional computational models for enterprise software are still to a great extent centralized. However, rapid growing of modern computation techniques and frameworks causes that contemporary software becomes more and more distributed. Towards development of new complete and coherent solution for distributed enterprise software construction, synthesis of three well-grounded concepts is proposed: Domain-Driven Design technique of software engineering, REST architectural style and actor model of computation. As a result new resources-based framework arises, which after first cases of use seems to be useful and worthy of further research.

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