Fractional maximal functions in metric measure spaces

We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to H\"older continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous

Fractional Hardy inequalities and visibility of the boundary

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.Comment: 30 pages, 3 figures. Minor revisions to the previous version. To be published in Studia Mat

Business process modeling and simulation

The textbook provides the essentials of the Business Process (BP) Modeling and Simulation (M&S) from the verbal BP description to the formulation of the mathematical scheme of the model and the simulation program. Both the analytical modeling and the simulation approaches to BP M&S are considered. Special attention is given to the theoretical and practical aspects of the BP M&S. The text covers the following topics: fundamentals of the BP M&S, conceptual modeling using IDEF3 standard, cost metrics and the activity based costing, analytical modeling (queuing networks, linear and dynamic programming), simulation with GPSS, timed Petri Nets, and Crystal Ball toolkits. Case studies include BP simulations with BPwin and GPSS. The intended readers are senior graduate students and junior postgraduate students of computer science and industrial management

Rädda jouren

Päivystyksen tulisi olla yksi terveydenhuollon käyntikorteista

Puolustusvoimien perusyksikön päällikkö työyhteisössä ja yksikön ulkopuolisissa sosiaalisissa verkostoissa

The aim of this paper is to analyze a company commander’s activity within his or her workplace community and external professional network in the Finnish Defence Forces (FDF) context. FDF’s company commander’s expert activity is thus networked and relational in nature. Such expertise can be seen as social interaction, knowledge sharing, and shared problem solving in interaction between individuals, communities and broader networks. These dynamics can be analyzed with the help of social networked analysis (SNA). Within SNA, these networks fall under the concept of egocentric networks. Workplace communities in FDF are not isolated from one another. Their development and pursuit of innovation depends on the fact that many of the participants are also members of other professional communities extending beyond the professional organization in question. New perspectives offered by professional development in interaction, knowledge sharing, knowledge communities and networking, mainly applied in business setting, have relevance in company commanders’ professional development too. It is also essential to understand how such pedagogical communities focusing on creation of new knowledge and novel social practices, function and how these kinds of communities can deliberately be cultivated. Also, a company commander’s personal life, formal and informal relations and accumulation of experience all affect her or his working behaviour. This is one of the realizations that broadens the perspective on professional development of company commanders from individual achievements to a larger framework of relations, where professional development is contributed to by the interaction of relationship of networks