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