Iterative Differential Equations and Finite Groups

It is an old question to characterize those differential equations or differential modules, respectively, whose solution spaces consist of functions which are algebraic over the base field. The most famous conjecture in this context is due to A. Gorthendieck and relates the algebraicity property with the p-curvature which apprears as the first integrability obstruction in characteristic p. Here we prove a variant of Grothendieck's conjecture for differential modules with vanishing higher integrability obstructions modulo p - these are iterative differential modules - and give some applications

From Frobenius Structures to Differential Equations

Frobenius structures are omnipresent in arithmetic geometry. In this note we show that over suitable rings, Frobenius endomorphisms define differential structures and vice versa. This includes, for example, differential rings in positive characteristic and complete non-archimedean differential rings in characteristic zero. Further, in the global case, the existence of sufficiently many Frobenius rings is related to algebraicity properties. These results apply, for example, to t-motives as well as to p-adic and arithmetic differential equations

Differential Equations and Finite Groups

This note is devoted to linear differential equations with finite Galois groups. It is a famous conjecture due to A. Grothendieck that the finiteness of the differential Galois group should be equivalent to the triviality of the p-curvature for almost all p. The p-curvature is just the first integrability obstruction for the reduced differential equation in characteristic p. In the case all such integrability obstructions vanish in characteristic p we obtain a so-called iterative differential equation or iterative differential module, respectively. For these a nice Picard-Vessiot theory has been developed by M. van der Put and the author. In particular, the differential Galois groups are linear algebraic groups and there is a Galois correspondence. Thus a natural question arises, wether there exists a reasonable reduction theory preserving Galois groups etc. The corresponding objects in characteristic zero are iterative differential modules over iterative differential rings. The latter are suitable Dedekind subrings of algebraic function fields over number fields, here called global differential rings. These and the corresponding global differential modules are studied in Chapter 1. Chapter 2 presents the construction of global Picard-Vessiot rings (PV-rings) over global differential rings and proves that such PV-rings are generated by globally bounded power series as introduced by G. Christol. In Chapter 3 the reduction of global differential modules and their PV-rings is studied. The main result is that a global PV-ring in characteristic zero is algebraic if and only if for almost all primes p the reduced PV-ring is algebraic. Moreover, for almost all p the reduced PV-ring and the PV-ring of the modulo p reduced global differential module coincide. According to Grothendieck's p-curvature conjecture all global PV-rings are algebraic. Using the result above, this fact might be proven directly. This would already imply a nice algebraicity criterion for formal power series over number fields used by G. Eisenstein and could become a significant step towards the proof of Grothendieck's conjecture

Effectief gebruik van social media ter bevordering van zelfgestuurd leren.

Onderzoek laat zien dat veel leraren experimenteren met de inzet van social media in hun lessen. Hierbij lijkt er een natuurlijke verbinding te bestaan tussen de inzet van social media en het bevorderen van zelfgestuurd leren. Duidelijke richtlijnen voor effectief gebruik van social media ontbreken echter. In deze studie formuleren we dergelijke richtlijnen en onderzoeken we de gebruiksmogelijkheden ervan in een empirische pilotstudie. Eerst wordt er een literatuurstudie uitgevoerd naar mogelijkheden om zelfgestuurd leren te faciliteren met behulp van social media. Vervolgens worden deze bevindingen vertaald naar richtlijnen. Tenslotte worden deze richtlijnen geïmplementeerd in een pabomodule. Hierbij wordt gezocht naar bevorderende en belemmerende factoren in het ontwerp, uitmondend in richtlijnen voor effectief gebruik van social media ter bevordering van zelfgestuurd leren

Essays in Political Economy: Drivers of Polarization

Diese Dissertation trägt zum Verständnis der zunehmenden Polarisierung von Gesellschaften bei. Das erste Kapitel konzentriert sich auf den Zustrom von Einwanderern als Ursache der Polarisierung. Die zunehmende Globalisierung führt zu einer wachsenden Zahl von Einwanderern, daher ist die Einwanderung zu einem zentralen und polarisierten Thema des politischen Diskurses geworden. In diesem Kapitel wird ein Shift-Share-Instrument eingesetzt, um die kausalen Auswirkungen des Zustroms von Einwanderern in die USA auf politische Ideologien zu bewerten. Es dokumentiert, dass Migration die Polarisierung von Politikern, die zwischen 1992 und 2016 für das Repräsentantenhaus kandidierten, verstärkte. Anschließend konzentriert sich die Studie auf Flüchtlinge, was durch neuartige Daten von über 3 Millionen Individuen ermöglicht wird. Die Ergebnisse spiegeln jene für Einwanderer wider und legen nahe, dass der Unterschied in der moralischen Rechtfertigung für die Aufnahme von Flüchtlingen sich nicht in einer anderen politischen Reaktion niederschlägt. Im zweiten Kapitel wird analysiert, ob die Einführung schnellen Internets indische Dörfer eint oder spaltet. Es nutzt die weltweit größte öffentliche Breitbandinitiative für den ländlichen Raum, die darauf abzielt, jedes indische Dorf an das Glasfasernetz anzuschließen. Um den kausalen Effekt des ländlichen Breitbandinternets zu ermitteln, nutzt dieses Papier die 2017 aufgetretenen räumlichen Diskontinuitäten zwischen Dörfern, die aufgrund der gestaffelten Einführung der Breitbandinitiative früh und spät angeschlossen wurden. Das Papier dokumentiert eine zunehmende Spaltung entlang mehrerer Dimensionen: Erstens nehmen Übergriffe und Ausschreitungen von Anhängern der hindu-nationalistischen Partei zu; zweitens werden Sozialleistungen in Jharkhand zunehmend nach religiösen Gesichtspunkten verteilt; drittens wählen in Jharkhand nicht-muslimische Dörfer die hindu-nationalistische Partei, während muslimische Dörfer die säkularen Parteien wählen. Im dritten Kapitel wird der politische Einfluss der Gewerkschaften untersucht. Der Arbeitsplatz ist nach Familie und Freunden der wichtigste Ort für politische Diskussionen und wird von den Gewerkschaften direkt beeinflusst. Dort können sie die ideologischen Positionen sowohl der gewerkschaftlich organisierten Arbeitnehmer als auch des nicht gewerkschaftlich organisierten Managements verändern. In diesem Beitrag werden die Auswirkungen der gewerkschaftlichen Organisierung auf die politischen Wahlkampfspenden von Arbeitnehmern und Managern im Zeitraum 1980-2016 in den Vereinigten Staaten auf betrieblicher Ebene analysiert. In einem Differenz-in-Differenzen-Design wird festgestellt, dass die Gewerkschaftsmitgliedschaft zu einer Linksverschiebung der Wahlkampfspenden führt. Die gewerkschaftliche Organisierung erhöht die Unterstützung für die Demokraten im Vergleich zu den Republikanern nicht nur unter den Arbeitnehmern, sondern auch unter den Managern, was gegen eine Zunahme der politischen Kluft zwischen den beiden Gruppen spricht. Diese Verschiebungen sind nicht auf Veränderungen in der Zusammensetzung der Belegschaft zurückzuführen, sondern sind auch auf individueller Ebene sichtbar.This thesis contributes to our understanding of the increasing polarization of societies. The first chapter focuses on immigration inflows as driver of polarization. As societies are faced with an increasing number of immigrants, immigration has become a central and polarized topic of political discourse. This chapter leverages a shift-share instrument to assess the causal impact of U.S. immigrant inflows on political ideologies. It documents that migration increased the polarization of politicians campaigning for the House of Representatives between 1992 and 2016. Subsequently, it focuses on refugees enabled by novel data covering over 3 million individuals. The results echo those for immigrants and suggest that the difference in the moral justification for welcoming refugees does not translate into a different political reaction. The second chapter analyzes whether the arrival of fast internet unites or divides Indian villages. It leverages the largest rural government broadband initiative in the world that aims to connect every Indian village to the fiber-optic network. To identify the causal effect of rural broadband internet, this paper exploits spatial discontinuities, which arose in 2017, between villages getting connected early and late due to the staggered roll-out of the broadband initiative. The paper documents an increase in divisions along several dimensions: First, assaults and riots of supporters of the Hindu nationalist party increase; second, welfare benefits in Jharkhand are increasingly distributed along religious lines; third, in Jharkhand, non-Muslim villages vote for the Hindu nationalist party while Muslim villages vote for the secular parties. The third chapter examines the political influence of labor unions. The workplace is behind family and friends the area most important for political discussions and it is directly influenced by unions. There, they may change the ideological positions of both unionizing workers and their non-unionizing management. This paper analyzes the workplace-level impact of unionization on workers’ and managers’ political campaign contributions over the 1980-2016 period in the United States. In a difference-in-differences design, it finds that unionization leads to a leftward shift of campaign contributions. Unionization increases the support for Democrats relative to Republicans not only among workers but also among managers, which speaks against an increase in political cleavages between the two groups. These shifts are not driven by compositional changes of the workforce but are also visible at the individual level.2023-10-1

The social embeddedness of academic online groups as a norm generating structure: A test of the Coleman model on norm emergence

This paper analyzes two questions. First, under which conditions does a norm emerge in academic online groups that prescribes members to help others during group discussions? Second, what effects does such a norm, and other social conditions, have on the contributing behavior of researchers during online discussions? It is argued that the Coleman model (1990) on the emergence of norms points to an important condition that facilitates the realization of such a norm. According to the Coleman model (1990) a dense network among members of a group tends to strengthen a group norm. The paper makes a distinction between different kinds of academic online groups. The criterion of the distinction is the extent to which within the membership a highly integrated research community exists. An online group with a highly integrated research community is called to have a high degree of social embeddedness of its online communication in offline networks. It is hypothesized that a high degree of embeddedness has a number of effects. A higher degree of embeddedness leads to a stronger help-prescribing norm. The stronger the norm the more researchers send online answers to questions of their co-members during public online discussions. Furthermore, a high degree of embeddedness increases the answering behavior of researchers directly because it provides opportunities to gain reputation within the academic community through contributing to the discussion. The study makes use of data that consist of a combination of survey data and observed data of the communication behavior of researchers in about 50 international academic emailing lists. The results provide evidence for the expected effect of embeddedness on the strength of the norm and for the effect of embeddedness on the answering behavior of researchers. The strength of the help-prescribing norm indirectly influences the answering behavior

The Church\u27s Approach to Death and the Funeral

This paper, therefore, will attempt to point out the approach which the church should take regarding the various cultural practices prevalent in the American funeral rite. After a brief historical perspective, it will examine the theological concepts of the body, death and the resurrection, and the psychological concepts of grief and mourning. With this as a basis for analysis, some of the cultural practices of the American funeral rite will be considered

Persuasion in the Art of Preaching for the Church

Throughout the following pages three major themes will be interwoven with the aspects of the preaching ministry mentioned above. The themes are pastoral in nature and have been formulated over many years in the parish ministry. In some ways, they are similar to the themes indicated in an isogogical study of a Scriptural text, as one studies (1) the addressees, (2) the content of the message, and (3) the approach or style of the writer. In a similar way, this paper will study the proclamation of the Word in relation to (1) the hearers, (2) the content of the message, and (3) the approach or manner of communication. These three areas of study, which are also the three goals of this paper, can be summarized in the following manner

New internet myths: no truth in a postfactual world?

The year 2016 has seen an unprecedented series of political campaigns that made use of the Internet, especially social media. Consequently, the Internet is increasingly being seen as a channel for influencing opinions, and it is being blamed for allowing spin doctors and other shady elements lurking at campaign trails in doing so without the necessity of content being related to facts. "Post-truth" was named the Oxford Dictionaries Word of the Year 2016, an adjective defined as "relating to or denoting circumstances in which objective facts are less influential in shaping public opinion than appeals to emotion and personal belief" (Oxford Dictionary, 2016). Relatedly, language institutions in several other languages followed suit, e.g. "postfaktisch" was also elected word of the year for German. The history of making new technologies responsible for societal developments beyond their actual impact is not new: when books were first printed, the invention of trains was thought to blind people, make them go crazy or cause female passengers' "uteruses ... fly out of [their] bodies" (Rooney, 2011). Old TV seems to get a break on its couch these days, while a crowd of teenage Internet services is being blamed for shattering the world's windows. In the current editorial, we take a close look at these "new Internet myths"

Article implace means journal impact

These days there is a lot of misunderstanding of scientometrics and we often see a confusion of the research with its indicators. Science ministries and university administrators try to push their country's or institution's "research impact" by telling researchers to increase numeric figures that were invented as proxies for later assessment. In obvious juxtaposition to common sense this even leads to direct orders to postdocs "to only publish in high impact journals" and not to engage in other important activities scientists of well-rounded stature will routinely perform, like publication in medium impact journals of their immediate field, in startup journals, in conference proceedings, of book chapters, as grey literature or intended for dissemination to the general public, reviewing, editing, writing blogs etc