On the extremals of the P\'olya-Szeg\H{o} inequality

The distance of an extremal of the P\'olya-Szeg\H{o} inequality from a translate of its symmetric decreasing rearrangement is controlled by the measure of the set of critical points.Comment: 17 pages, 3 figure

Green Public Procurements (GPP) as an Instrument of Implementation of Sustainable Development. Analysis of the Experience of the Łódź Region Local Government

This paper discusses the situation on the Polish green public procurements (GPP) market, with special emphasis on the results of a GPPinfoNET project realised in the Łódź region. The identification of the main barriers hindering the application of GPP in the Polish practice is the departure point to formulating recommendations concerning organisational and legal changes which would make it possible to increase the share of GPP in the Polish economic practice. Implementation of green public procurement is considered as an important element of sustainable development.W artykule przedmiotem analizy jest sytuacja na polskim rynku zielonych zamówień publicznych, ze szczególnym uwzględnieniem efektów projektu GPPinfoNET realizowanego w regionie łódzkim. Punktem wyjścia do sformułowania rekomendacji dotyczących zmian organizacyjnych i prawnych służących popularyzacji ZZP jest identyfikacja głównych barier hamujących stosowanie takich zamówień w polskiej praktyce gospodarczej. Wdrażanie zielonych zamówień publicznych jest traktowane jako ważny element realizacji zrównoważonego rozwoju

Production for a green economy

In the chapter are discussed new approaches of production development in order to achieve the objectives of sustainable development and put the green economy into practice. Conventional approaches to the production must be re-oriented towards the promotion of renewable, cleaner and more effi technologies aimed at the conservation of all natural resources. This requires a new approach to the design of products and their production, and requires the inclusion of post-industrial and post-consumer residues into permanent circulation and the development of eco-innovative management patterns. In the implementation of such solutions the “cradle to cradle” approach could be useful.Wydanie współfinansowane ze środków Miasta Łodzi w ramach zadania “Współpraca z wyższymi uczelniami” – umowa 100/03/201

Convergence to equilibrium for a thin film equation on a cylindrical surface

The degenerate parabolic equation u_t + [u^3(u_xxx + u_x - sin x)]_x=0 models the evolution of a thin liquid film on a stationary horizontal cylinder. It is shown here that for each given mass there is a unique steady state, given by a droplet hanging from the bottom of the cylinder that meets the dry region at the top with zero contact angle. The droplet minimizes the energy and attracts all strong solutions that satisfy certain energy and entropy inequalities. The distance of any solution from the steady state decays no faster than a power law.Comment: 26 pages, 6 figures. This is a greatly expanded version of our previous submission [arXiv:1009.4092v1]. The main result on convergence to equilbrium is new, and the bounds on the rate of convergence have been simplified. For the second version, we have changed the title, corrected Lemma 2.3, rewrittenSection 3, and added several reference