The origin of high-resolution IETS-STM images of organic molecules with functionalized tips

Recently, the family of high-resolution scanning probe imaging techniques using decorated tips has been complimented by a method based on inelastic electron tunneling spectroscopy (IETS). The new technique resolves the inner structure of organic molecules by mapping the vibrational energy of a single carbonmonoxide (CO) molecule positioned at the apex of a scanning tunnelling microscope (STM) tip. Here, we explain high-resolution IETS imaging by extending the model developed earlier for STM and atomic force microscopy (AFM) imaging with decorated tips. In particular, we show that the tip decorated with CO acts as a nanoscale sensor that changes the energy of the CO frustrated translation in response to the change of the local curvature of the surface potential. In addition, we show that high resolution AFM, STM and IETS-STM images can deliver information about intramolecular charge transfer for molecules deposited on a~surface. To demonstrate this, we extended our numerical model by taking into the account the electrostatic force acting between the decorated tip and surface Hartree potential.Comment: 5 pages, 4 figure

H2_2 dissociation over Au-nanowires and the fractional conductance quantum

The dissociation of H$_2$ molecules on stretched Au nanowires and its effect on the nanowire conductance are analyzed using a combination of Density Functional (DFT) total energy calculations and non-equilibrium Keldish-Green function methods. Our DFT simulations reproduce the characteristic formation of Au monoatomic chains with a conductance close to % the conductance quantum $G_0 = 2e^2/h$. These stretched Au nanowires are shown to be better catalysts for H$_2$ dissociation than Au surfaces. This is confirmed by the nanowire conductance evidence: while not affected practically by molecular hydrogen, atomic hydrogen induces the appearance of fractional conductances ($G \sim 0.5 G_0$) as observed experimentally.Comment: 4 pages, 3 figure

Theoretical analysis of electronic band structure of 2-to-3-nm Si nanocrystals

We introduce a general method which allows reconstruction of electronic band structure of nanocrystals from ordinary real-space electronic structure calculations. A comprehensive study of band structure of a realistic nanocrystal is given including full geometric and electronic relaxation with the surface passivating groups. In particular, we combine this method with large scale density functional theory calculations to obtain insight into the luminescence properties of silicon nanocrystals of up to 3 nm in size depending on the surface passivation and geometric distortion. We conclude that the band structure concept is applicable to silicon nanocrystals with diameter larger than $\approx$ 2 nm with certain limitations. We also show how perturbations due to polarized surface groups or geometric distortion can lead to considerable moderation of momentum space selection rules

Design of cutting unit

Tato práce pojednává o konstrukčním řešení řezacího válce, včetně návrhu jeho pohonu a odsávacího systému pro flexotiskový stroj Premia společnosti Soma spol. s r.o.. První část pojednává o technologii flexotisku a obecně o dané problematice ořezu a odsávání materiálu. Další část se zabývá optimalizací těchto systémů, včetně výsledného konstrukčního návrhu. Hlavním výstupem práce jsou výkresy sestavení uvedené v přílohách.This thesis deals with a structural design of a cutting roller including a proposal for its drive and exhaust system of the flexography machine Premia produced by Soma spol. s r.o. company. The first part discusses the technology of flexography and about the issue of cropping and extraction of material in general. Another part discusses the optimization of these systems, including the final engineering design. The main outcome of this thesis are drawings of assemblies listed in the annexes.

On the Beer index of convexity and its variants

Let $S$ be a subset of $\mathbb{R}^d$ with finite positive Lebesgue measure. The Beer index of convexity $\operatorname{b}(S)$ of $S$ is the probability that two points of $S$ chosen uniformly independently at random see each other in $S$. The convexity ratio $\operatorname{c}(S)$ of $S$ is the Lebesgue measure of the largest convex subset of $S$ divided by the Lebesgue measure of $S$. We investigate the relationship between these two natural measures of convexity. We show that every set $S\subseteq\mathbb{R}^2$ with simply connected components satisfies $\operatorname{b}(S)\leq\alpha\operatorname{c}(S)$ for an absolute constant $\alpha$, provided $\operatorname{b}(S)$ is defined. This implies an affirmative answer to the conjecture of Cabello et al. that this estimate holds for simple polygons. We also consider higher-order generalizations of $\operatorname{b}(S)$. For $1\leq k\leq d$, the $k$-index of convexity $\operatorname{b}_k(S)$ of a set $S\subseteq\mathbb{R}^d$ is the probability that the convex hull of a $(k+1)$-tuple of points chosen uniformly independently at random from $S$ is contained in $S$. We show that for every $d\geq 2$ there is a constant $\beta(d)>0$ such that every set $S\subseteq\mathbb{R}^d$ satisfies $\operatorname{b}_d(S)\leq\beta\operatorname{c}(S)$, provided $\operatorname{b}_d(S)$ exists. We provide an almost matching lower bound by showing that there is a constant $\gamma(d)>0$ such that for every $\varepsilon\in(0,1)$ there is a set $S\subseteq\mathbb{R}^d$ of Lebesgue measure $1$ satisfying $\operatorname{c}(S)\leq\varepsilon$ and $\operatorname{b}_d(S)\geq\gamma\frac{\varepsilon}{\log_2{1/\varepsilon}}\geq\gamma\frac{\operatorname{c}(S)}{\log_2{1/\operatorname{c}(S)}}$.Comment: Final version, minor revisio