Antisquares and Critical Exponents

The complement $\bar{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An antisquare is a nonempty word of the form $x\, \bar{x}$. In this paper, we study infinite binary words that do not contain arbitrarily large antisquares. For example, we show that the repetition threshold for the language of infinite binary words containing exactly two distinct antisquares is $(5+\sqrt{5})/2$. We also study repetition thresholds for related classes, where "two" in the previous sentence is replaced by a large number. We say a binary word is good if the only antisquares it contains are $01$ and $10$. We characterize the minimal antisquares, that is, those words that are antisquares but all proper factors are good. We determine the the growth rate of the number of good words of length $n$ and determine the repetition threshold between polynomial and exponential growth for the number of good words

Decision Algorithms for Ostrowski-Automatic Sequences

We extend the notion of automatic sequences to a broader class, the Ostrowski-automatic sequences. We develop a procedure for computationally deciding certain combinatorial and enumeration questions about such sequences that can be expressed as predicates in first-order logic. In Chapter 1, we begin with topics and ideas that are preliminary to this work, including a small introduction to non-standard positional numeration systems and the relationship between words and automata. In Chapter 2, we define the theoretical foundations for recognizing addition in a generalized Ostrowski numeration system and formalize the general theory that develops our decision procedure. Next, in Chapter 3, we show how to implement these ideas in practice, and provide the implementation as an integration to the automatic theorem-proving software package -- Walnut. Further, we provide some applications of our work in Chapter 4. These applications span several topics in combinatorics on words, including repetitions, pattern-avoidance, critical exponents of special classes of words, properties of Lucas words, and so forth. Finally, we close with open problems on decidability and higher-order numeration systems and discuss future directions for research

Chemical Bonding in Solids

This chapter discusses the various classes of hydride compounds, with a special focus on saline and metallic hydrides as well as oxyhydrides. It includes the following topics: thermodynamic stability, crystal chemistry, synthesis, and physical properties. The chapter also highlights recent progress in understanding hydride ion mobility in alkaline earth hydrides. It further deals with hydride compounds and in particular those containing alkali, alkaline earth, and transition and rare earth metals. The saline hydrides, that is, AH and AeH2 (with A=Li, Na, K, Rb, and Cs; Ae=Mg, Ca, Sr, and Ba) are proper ionic materials, in which hydrogen is present as hydride anions, H−. Saline hydrides show many similarities with their halide analogues, especially concerning crystal and electronic structures and, perhaps to a lesser extent, physical attributes such as brittleness, hardness, and optical properties

Evaluation of solder joints on aluminum surfaces for the interconnection of silicon solar cells

In this thesis, direct soldering of aluminum is investigated, with a special focus on appplication in the photovoltaic industry. The native Al2O3 layer impedes the solderability of Al components. However, strong solder joints can be formed when suitable surface coatings are used. The formation of solder joints and the relevant fundamental properties of these joints and coatings are evaluated.Im Rahmen dieser Dissertation wird die direkte Lötbarkeit von Aluminium, mit dem Ziel der Anwendung in der Photovoltaik Industrie, untersucht. Die natürliche Al2O3 Oxidschicht erschwert das Weichlöten von Aluminiumbauteilen. Dennoch ist es möglich, unter der Verwendung einer geeigneten Oberflächenbeschichtung, starke Lötverbindungen auszubilden. Die Lötstellen, deren relevante Eigenschaften, sowie die der Beschichtungen, werden in der vorliegenden Arbeit evaluiert