Differences of weighted composition operators between the Fock spaces

We study some important topological properties such as boundedness, compactness and essential norm of differences of weighted composition operators between Fock spacesComment: 10 page

Weighted composition operators between different Fock spaces

We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete descriptions of path connected components and isolated points of the space of composition operators and the space of nonzero weighted composition operators

Frames and operators in Schatten classes

Let $T$ be a compact operator on a separable Hilbert space $H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten class $S_p$ if and only if $\{\|Tf_n\|\}\in \ell^p$ for \emph{every} frame $\{f_n\}$ in $H$; and for $0<p\le2$, $T$ belongs to $S_p$ if and only if $\{\|Tf_n\|\}\in\ell^p$ for \emph{some} frame $\{f_n\}$ in $H$. Similar conditions are also obtained in terms of the sequence $\{\}$ and the double-indexed sequence $\{\}$.Comment: 27 page

AUTODESK® GREEN BUILDING STUDIO FOR AN ENERGY-EFFICIENT, SUSTAINABLE BUILDING

The thesis introduced AutoDesk® Green Building Studio (GBS) which is a software for analyzing the whole building. It gives the results of energy consumption such as water usage and costs, natural ventilation potential, carbon emissions based on an actual model, local energy sources and weather data. The aim of the research was to optimize a plan to achieve an energy-efficient, sustainable building by multiple choices of alternative designs. In addition, the comparison between AutoDesk® Green Building Studio and Graphisoft ArchiCad Ecodesigner Star was done. An existing design of a residential house was modeled by the parent prod-uct: AutoDesk® Revit and was analyzed by the GBS on a web-based analysis service (https://gbs.autodesk.com). The information on typical elements of the building was presented. The web-based service features with all results and alternative designs were also described. In conclusion, the best energy efficient, sustainable design was recom-mended to architects for future projects and the software GBS and its functions and features on a web-based service were introduced as a suggestion

On a sub-supersolution method for the prescribed mean curvature problem

summary:The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established