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In practice, graphs often occur as perturbed product structures, so-called approximate graph products. The practical application of the well-known prime factorization algorithms is therefore limited, since most graphs are prime, although they can have a product-like structure. This work is concerned with the strong graph product. Since strong product graphs G contain subgraphs that are itself products of subgraphs of the underlying factors of G, we follow the idea to develop local approaches that cover a graph by factorizable patches and then use this information to derive the global factors. First, we investigate the local structure of strong product graphs and introduce the backbone B(G) of a graph G and the so-called S1-condition. Both concepts play a central role for determining the prime factors of a strong product graph in a unique way. Then, we discuss several graph classes, in detail, NICE, CHIC and locally unrefined graphs. For each class we construct local, quasi-linear time prime factorization algorithms. Combining these results, we then derive a new local prime factorization algorithm for all graphs. Finally, we discuss approximate graph products. We use the new local factorization algorithm to derive a method for the recognition of approximate graph products. Furthermore, we evaluate the performance of this algorithm on a sample of approximate graph products.

The study of integral operators on spaces of analytic functions has been considered for the past few decades. However, most of the studies in this line are based on spaces of analytic functions of the unit disc. For the analytic spaces of the upper half-plane, the literature is still scanty. Most notable is the recent work of Siskakis and Arvanitidis concerning the classical Ces`aro operator on Hardy spaces of the upper half-plane. In this dissertation, we characterize all continuous one-parameter groups of automorphisms of the upper halfplane according to the nature and location of their fixed points into three distinct classes, namely, the scaling, the translation, and the rotation groups. We then introduce the associated groups of weighted composition operators on both Hardy and weighted Bergman spaces of the half-plane. Interestingly, it turns out that these groups of composition operators form three strongly continuous groups of isometries. A detailed analysis of each of these groups of isometries is carried out. Specifically, we determine the spectral properties of the generators of every group, and using both spectral and semigroup theory of Banach spaces, we obtain concrete representations of the resolvents as integral operators on both Hardy and Bergman spaces of the half-plane. For the scaling group, the resulting resolvent operators are exactly the Ces`aro-like operators. The spectral properties of the obtained integral operators is also determined. Finally, we detail the theory of both Szeg¨o and Bergman projections of the half-plane, and use it to determine the duality properties of these spaces. Consequently, we obtain the adjoints of the resolvent operators on the reflexive Hardy and Bergman spaces of the half-plane.

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Gender provisions have the overarching goal of enhancing gender equality, however few peace agreements include strong gender provisions. The presence of strong gender provisions in ceasefire agreements has crucial implications in the immediate and post-conflict phase in improving women’s situation. I use structured, focused comparison in this study to explore when and how strong gender provisions on violence against women are adopted. I focus on conflicts with a high prevalence of sexual violence and contexts where women mobilize in the conflict to advocate for women’s rights. I demonstrate the relationship between international involvement and strong gender provisions. I argue that in civil wars with a high level of international involvement in support of peace, ceasefire agreements are more likely to include strong gender provisions on violence against women. This is possible through the mechanism of international actors serving as brokers for the women’s movement that is already mobilized to access and influence the peace process. This mechanism is particularly crucial for autocratic countries where women’s mobilization is not sufficient to lead to strong gender provisions. However, the findings are applicable to countries with other regime types.

This study assessed the influence of language on the ability of children identified as being at risk for internalizing behavior disorders to successfully participate in a social skills intervention program. Fourth and fifth grade students participated in Strong Kids: A Social and Emotional Learning Curriculum in Grades 4-8, a program which promotes emotional resiliency. The Clinical Evaluation of Language Fundamentals-Fourth Edition (CELF-4) and Children's Communication Checklist-Second Edition (CCC-2) were both completed to obtain a global language score and pragmatic language score. The Teacher's Report Form (TRF), a shortened 10-item version of the Internalizing Student Symptom Scale (ISSC), and a 20-item knowledge based assessment relating to the Strong Kids curriculum were completed prior to and after the intervention. These behavioral assessments were administered in order to determine improvement in academic performance, adaptive functioning, and behavioral/emotional problems with relation to language functioning. It was found that children with higher general language abilities made significantly positive improvements with regard to withdrawal than children with lower general language abilities on measures taken prior to and directly after the Strong Kids curriculum. Additionally, the ISSC revealed that children with lower general language abilities rated themselves as having significantly more positive changes in behavior than children with higher general language abilities on measures taken prior to and six weeks following the Strong Kids curriculum. Pragmatic functioning, determined by the CCC-2, was not associated with significant behavioral improvements between children with high and low pragmatic language skills.

Disorder-induced heating (DIH) is a nonequilibrium, ultrafast relaxation process that occurs when laser-cooled atoms are photoionized to make an ultracold plasma. Its effects dominate the ion motion during the first 100 ns of the plasma evolution. Using tools of atomic physics we study DIH with ns time resolution for different plasma densities and temperatures. By changing the frequency of the laser beam we use to probe the ions, we map out the time evolution of the velocity distribution. We can compare this to a fluorescence simulation in order to more clearly determine the relationship between the fluorescence signal and the velocity distribution. In this study we observe and characterize effects due to electron screening on the ions during the equilibration process.

Composite cascode stages have been used in operational amplifier designs to achieve ultra-high gain at very low power. The flexibility and simplicity of the stage makes it an appealing choice for low power op-amp designs. Op-amp design using the composite cascode stage is often made more difficult through the lack of a design process. A design process to aid in the selection of the MOSFET dimensions is provided in this thesis. This process includes a table-based method for selection of the widths and lengths of the MOSFETs used in the composite cascode stage. Equations are also derived for the gain, bandwidth, and noise of the composite cascode stage with each of the devices operating in the various regions of inversion.