The German Academic Exchange Service, or DAAD (German: Deutscher Akademischer Austauschdienst), was founded in 1925 and is the largest German support organisation in the field of international academic co-operation.
The distinguishing number of a permutation group G⩽(Ω) is the minimum number of colours needed to colour Ω in such a way that the only colour preserving element of G is the identity. The distinguishing number of a graph is the distinguishing number of its automorphism group (as a permutation group on vertices). We determine the distinguishing number of the complete bipartite graphs K_n,n and the crown graphs K_n,n-nK_2, as well as the distinguishing number of some `large' subgroups of their automorphism groups, that is, the subgroups that are vertex- and edge-transitive and such that the induced action on each bipart is (n) or (n). We show that, if G is a `large' group of automorphisms of K_n,n, then n-1⩽ D(G) ⩽ n+1. Similarly, if G is a `large' group of automorphisms of a crown graph, then ⌈√(n-1)⌉⩽ D(G)⩽⌊√(n)⌋+1. Keywords: complete bipartite graph; crown graph; distinguishing number; symmetric group; alternating group
Extending earlier results of Nešetřil and Rödl [Selective graphs and hypergraphs, Ann. Discrete Math. 3 (1978), 181--189], we show that for every ordered graph $F$ there exist an ordered graph $H$ and a system $\mathscr{H}_F$ of induced copies of $F$ such that every colouring of the edges of $H$ yields a canonically coloured copy of $F$ from $\mathscr{H}_F$ and any two copies from $\mathscr{H}_F$ intersect either in a vertex or an edge or not at all. As a consequence, this allows us to construct, for any given ordered graph $F$, canonical Ramsey graphs $H$ enjoying additional structural properties. In particular, $H$ can have the same clique number as $F$ and, provided $F$ is not bipartite, the same odd girth. Moreover, if $F$ is connected, then the copies of $F$ from $\mathscr{H}_F$ are not only induced, but their pairs of vertices also have the same distances in $H$ as in $F$.
We analyze an inverse problem for determining the piston speed and the associated flow field from a prescribed leading shock and the initial data in a shock tube. The gas flow is described by the isentropic Euler equations (i.e., the p-system), while the trajectory of the leading shock is prescribed as a given Lipschitz curve. Under an Oleĭnik-type entropy condition on the leading shock, we develop a modified wavefront tracking scheme to construct the flow field behind the shock. This construction enables us to determine the corresponding piston speed and the associated flow field.
The paper takes a historical look at the DAAD, which will celebrate its 100th anniversary in 2025. Using language policy as an example, a potential research project is outlined alongside a number of hypotheses: How does an institution like DAAD position itself between academic and political interests? How has it managed, particularly since 1950, when the DAAD was reestablished as an association of German universities and thus a politically independent organization, to maintain this independence while simultaneously playing a role in the foreign science policy of the Federal Republic of Germany? To what extent do political trends influence the development of funding programs and the expansion of the 'toolbox' for scientific internationalization? The paper is based on the hypothesis that DAAD's 'language policy' is indeed subject to political trends both within Germany and internationally, but that it has repeatedly succeeded in setting independent priorities-an achievement that is key to the DAAD's 100-year success story.
Let G be a totally disconnected locally compact (tdlc) group. The contraction group con(g) of an element g∈ G is the set of all h∈ G such that g^n h g^-n→ 1_G as n →∞. The nub of g can then be characterized as the intersection nub(g) of the closures of con(g) and con(g^-1). Contraction groups and nubs provide important tools in the study of the structure of tdlc groups, as already evidenced in the work of G. Willis. It is known that nub(g) = {1} if and only if con(g) is closed. In general, contraction groups are not closed and computing the nub is typically a challenging problem. Maximal Kac-Moody groups over finite fields form a prominent family of non-discrete compactly generated simple tdlc groups. In this paper we give a complete description of the nub of any element in these groups.
