We are interested in algorithms for constructing surfaces Γ of possibly small measure that separate a given domain Ω into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians, p → 1, under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients.
A topological space X is called base-base paracompact (John E. Porter) if it has an open base B such that every base B ′ ⊆ B has a locally finite subcover C ⊆ B′ . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.
We present a new technological approach for in situ investigation of long-term impacts of elevated CO2 concentration (EC) on juvenile forests characterised by an intensive community level and canopy closure phase. Construction of the glass domes is based on the properties of earlier tested open-top chambers (OTCs). An air climatisation device together with an adjustable window system, that forms the shell cover of the domes, is able to keep the required [CO2] in both time and spatial scales with the relatively small consumption of supplied CO2. This is achieved by half-closing the windows on the windward side. We evidenced good coupling of treated trees to the atmosphere, including mutual interactions among trees. The semi-open design of the domes moderates the problems of strong wind, humidity, and temperature gradients associated with OTCs. The frequency distributions of the environmental variations within the domes indicate that: air temperature is maintained within the ambient range ±1.0 °C for ca. 80 % of the time, and changes in the relative air humidity vary from -15 to 0 % for ca. 82 % of the time. The most important chamber effect is associated with the penetration of solar irradiance, which is reduced by 26 % compared to the open condition outside the domes. The dimensions of the domes are 10×10 m in length and 7 m high in the central part. The experiment was done in three identical stands of twelve-year-old Norway spruce trees. The 56 trees are planted at two different spacings to estimate the impacts of stand spatial structure in relation to EC. and O. Urban ... [et al.].
Significant impact on navigation operation by hydropower plant (HPP) operation is mostly in diversion channels of hydropower plants, when these channels are used for navigation as well. It is caused by sudden changes in flow rate of hydropower plants, which is connected to providing of support serveces for electric power system. The objective of the esearch is t determine limits of acceptable hydropower plant operation or propose pecautions which enable harmonizaton of opposing interests of navigation and power generation. and Obsahuje seznam literatury