Sharp two-sided heat kernel estimates of twisted tubes and applications

We prove on-diagonal bounds for the heat kernel of the Dirichlet Laplacian $-\Delta^D_\Omega$ in locally twisted three-dimensional tubes $\Omega$. In particular, we show that for any fixed $x$ the heat kernel decays for large times as $\mathrm{e}^{-E_1t}\, t^{-3/2}$, where $E_1$ is the fundamental eigenvalue of the Dirichlet Laplacian on the cross section of the tube. This shows that any, suitably regular, local twisting speeds up the decay of the heat kernel with respect to the case of straight (untwisted) tubes. Moreover, the above large time decay is valid for a wide class of subcritical operators defined on a straight tube. We also discuss some applications of this result, such as Sobolev inequalities and spectral estimates for Schr\"odinger operators $-\Delta^D_\Omega-V$.Comment: To appear in Arch. Rat. Mech. Ana

Merging Tasks with Non-Interfering Requests for the System Baker

Obsahem práce je návrh formátu pro zápis parametrů a požadavků jednotlivých úloh určených pro systém Beaker a návrh a implementace programu, který na základě vyloučení možných kolizních požadavků sloučí úlohy definované na vstupu do souboru úloh, jež je možné spouštět společně. Výstupem je formát spustitelný v systému Beaker. Práce popisuje instalaci operačního systému, na kterém definuje kolizní požadavky. V práci je popsán způsob zadávání a spouštění úloh v systému Beaker. V závěru je provedeno testování vytvořeného programu.The goal of this thesis is to design a format for entering parameters and requirements of individual tasks intended for the Beaker system and to design a program that merges tasks defined upon input based on elimination of possible collision requirements into collection of tasks that can be run together. The output format should be acceptable by the Beaker system. The thesis describes installation of the operating system on which collision requirements are defined. The thesis describes how to specify and run tasks in the Beaker system. The results of the program testing are shown in the thesis' conclusion.

On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator III: Magnetic fields that change sign

We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kova\v{r}\'ik-Portmann and Helffer-Sundqvist for the asymptotics of the ground state energy in the semi-classical limit when the magnetic field has constant sign. In this paper, we focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter tends to zero and give lower bounds and upper bounds for this decay rate. Concrete examples of magnetic fields changing sign on the unit disc are discussed. Various natural conjectures are disproved and this leaves the research of an optimal result in the general case still open.Comment: 20 pages, 8 figure

An Interactive Simulator for Data-flow Graphs

Grafy toku dat jsou často používány při návrhu hardware. Jsou však vhodné také pro provádění hlubších analýz návrhů (např. funkční a formální verifikace). Simulátor prezentovaný v této práci vzniká jako podpůrný nástroj pro verifikační prostředí HADES. Cílem simulátoru je snížit potřebný čas a zvýšit kvalitu procesu verifikace. Pro efektivní provádění simulace byl navržen a implementován simulační algoritmus, který díky eliminaci nadbytečných vyhodnocení šetří výpočetní čas. Simulátor je vybaven několika výstupními rozhraními, která jsou připojena k simulačnímu jádru. První rozhraní poskytuje přímý výstup simulace v textové podobě. K němu existuje také interaktivní varianta, která dovoluje uživateli řídit běh simulace a manipulovat se stavem modelu. Třetí vytváří plnohodnotné uživatelské rozhraní určené pro vizualizaci  průběhu simulace.Data-flow graphs are often used by hardware designers. Such graph representation is also very useful for performing deeper analysis of a design (including functional or formal verification). Simulator presented in this thesis is a support tool for verification environment HADES. The goal of the simulator is to decrease necessary time and increase quality of the verification process. To perform a simulation efficiently, a specific simulation algorithm which saves computation time by eliminating redundant evaluations has been introduced. The simulator is equiped with several output interfaces connected to a single simulation core. One output interface provides direct simulation output in text format. The second is also textual, but allows user to control the simulation. Finally, the third forms a graphical interface that visualizes simulation results.

Description of \u3cem\u3eTityus mraceki\u3c/em\u3e sp. n. from Colombia and Synonymization of \u3cem\u3eT. meridanus\u3c/em\u3e González-Sponga with \u3cem\u3eT. nematochirus\u3c/em\u3e Mello-Leitão (Scorpiones: Buthidae)

Tityus (Archaeotityus) mraceki sp. n. from Colombia is described. It differs from other species of the subgenus Archaeotityus by unique sexual dimorphism expressed in the male having a longer metasoma and a narrower chela of the pedipalp. The synonymization of T. meridanus González-Sponga, 1981 with T. nematochirus Mello-Leitão, 1941 is based on morphological and color variation present in a single litter consisting of 33 individuals

Scorpions of the Horn of Africa (Arachnida, Scorpiones). Part XIV. \u3cem\u3eHottentotta somalicus\u3c/em\u3e sp. n. (Buthidae) from Somalia

Hottentotta somalicus sp. n. from Somalia is described and fully complemented with color photos. Morphologically it is similar to H. polystictus (Pocock, 1896). These two species have very narrow metasomal segments (1.63–1.73 in both sexes versus 1.31–1.61 in both sexes of other Hottentotta species from the Horn of Africa). H. polystictus and H. somalicus sp. n. occur in separate areas (Somaliland versus Somalia) and can be differentiated by color