From Pappus Theorem to parameter spaces of some extremal line point configurations and applications

In the present work we study parameter spaces of two line point configurations introduced by B\"or\"oczky. These configurations are extremal from the point of view of Dirac-Motzkin Conjecture settled recently by Green and Tao. They have appeared also recently in commutative algebra in connection with the containment problem for symbolic and ordinary powers of homogeneous ideals and in algebraic geometry in considerations revolving around the Bounded Negativity Conjecture. Our main results are Theorem A and Theorem B. We show that the parameter space of what we call $B12$ configurations is a three dimensional rational variety. As a consequence we derive the existence of a three dimensional family of rational $B12$ configurations. On the other hand the moduli space of $B15$ configurations is shown to be an elliptic curve with only finitely many rational points, all corresponding to degenerate configurations. Thus, somewhat surprisingly, we conclude that there are no rational $B15$ configurations.Comment: 17 pages, v.2. title modified, material reorganized, introduction new rewritten, discussion more streamline

Energy efficient house with design office

Bakalářská práce "Energeticky efektivní dům s projekční kanceláří" je zpracován ve formě projektové dokumentace dle platných přepisů. Objekt je navržen jako dvoupodlažní podsklepený rodinný dům s obytným podkrovím, s jednopodlažní nepodsklepenou provozovnou a garáží s plochou střechou. Objekt je založen na základových pásech, svislé konstrukce jsou zděné, stropy a nosná konstrukce ploché střech je monolitická, konstrukci šikmé střechy tvoří dřevěný krov. Objekt je řešen jako nízkoenergetický dům.The Bachelor´s thesis Energy efficient house with desing office is made as building documentation in agreenment whith standarts and legal norms and acts. House is desinged as two floored basement house with pitched roof and one floored cellarless, flat roofe part with workshop and garage. The construction is based on a concrete strip foundation. The building is made of ceramic block, the ceiling and flat roof is designed as monolithic construcion, pitched roof is made as wooden roof construction. House is projected as Low energy detached house.