From evolution to co-evolution – An empirical study of the role of innovation, policy and public research in industrial dynamics

In the past decades since Schumpeter’s influential writings economists have pursued research to examine the role of innovation in certain industries on firm as well as on industry level. Researchers describe innovations as the main trigger of industry dynamics, while policy makers argue that research and education are directly linked to economic growth and welfare. Thus, research and education are an important objective of public policy. Firms and public research are regarded as the main actors which are relevant for the creation of new knowledge. This knowledge is finally brought to the market through innovations. What is more, policy makers support innovations. Both actors, i.e. policy makers and researchers, agree that innovation plays a central role but researchers still neglect the role that public policy plays in the field of industrial dynamics. Therefore, the main objective of this work is to learn more about the interdependencies of innovation, policy and public research in industrial dynamics. The overarching research question of this dissertation asks whether it is possible to analyze patterns of industry evolution – from evolution to co-evolution – based on empirical studies of the role of innovation, policy and public research in industrial dynamics. This work starts with a hypothesis-based investigation of traditional approaches of industrial dynamics. Namely, the testing of a basic assumption of the core models of industrial dynamics and the analysis of the evolutionary patterns – though with an industry which is driven by public policy as example. Subsequently it moves to a more explorative approach, investigating co-evolutionary processes. The underlying questions of the research include the following: Do large firms have an advantage because of their size which is attributable to cost spreading? Do firms that plan to grow have more innovations? What role does public policy play for the evolutionary patterns of an industry? Are the same evolutionary patterns observable as those described in the ILC theories? And is it possible to observe regional co-evolutionary processes of science, innovation and industry evolution? Based on two different empirical contexts – namely the laser and the photovoltaic industry – this dissertation tries to answer these questions and combines an evolutionary approach with a co-evolutionary approach. The first chapter starts with an introduction of the topic and the fields this dissertation is based on. The second chapter provides a new test of the Cohen and Klepper (1996) model of cost spreading, which explains the relationship between innovation, firm size and R&D, at the example of the photovoltaic industry in Germany. First, it is analyzed whether the cost spreading mechanism serves as an explanation for size advantages in this industry. This is related to the assumption that the incentives to invest in R&D increase with the ex-ante output. Furthermore, it is investigated whether firms that plan to grow will have more innovative activities. The results indicate that cost spreading serves as an explanation for size advantages in this industry and, furthermore, growth plans lead to higher amount of innovative activities. What is more, the role public policy plays for industry evolution is not finally analyzed in the field of industrial dynamics. In the case of Germany, the introduction of demand inducing policy instruments stimulated market and industry growth. While this policy immediately accelerated market volume, the effect on industry evolution is more ambiguous. Thus, chapter three analyzes this relationship by considering a model of industry evolution, where demand-inducing policies will be discussed as a possible trigger of development. The findings suggest that these instruments can take the same effect as a technical advance to foster the growth of an industry and its shakeout. The fourth chapter explores the regional co-evolution of firm population size, private-sector patenting and public research in the empirical context of German laser research and manufacturing over more than 40 years from the emergence of the industry to the mid-2000s. The qualitative as well as quantitative evidence is suggestive of a co-evolutionary process of mutual interdependence rather than a unidirectional effect of public research on private-sector activities. Chapter five concludes with a summary, the contribution of this work as well as the implications and an outlook of further possible research.

Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

New calculations of P(b) curves for 1s_\sigma excitation in low-Z (Z\le10) ion-atom scattering

Ab initio fully relativistic SCF molecular calculations of energy eigenvalues as well as coupling-matrix elements are used to calculate the 1s_\sigma excitation differential cross section for Ne-Ne and Ne-O in ion-atom collisions. A relativistic perturbation treatment which allows a direct comparison with analogous non-relativistic calculations is also performed.