Nonlinear differential equations satisfied by certain classical modular forms

A unified treatment is given of low-weight modular forms on ?? ₀(N), N = 2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under ?? ₀(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard?CFuchs equations of triangle subgroups of PSL(2, R), which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with ??(1) is treated.     

Cyclic normal subgroups of generalized Baumslag–Solitar groups

The centers and cyclic radicals of generalized Baumslag–Solitar groups (GBS-groups) are studied. Criteria for their non-triviality are found and an algorithm to compute the center and cyclic radical is given. In addition, for each unimodular GBS-group, a GBS-cover, i.e., a GBS-group in whose underlying graph the weights around each vertex are constant in absolute value, is constructed. These groups are then characterized by a minimality property.     

The decay of theI π=8+ isomer in100Cd-neutron particle and proton hole states

The γ-decay and half life of the t_1/2=60(3) ns I^π=8⁺ isomer in¹⁰⁰Cd have been studied with a recoil catcher setup inside the multidetector π-array OSIRIS. Evaporation neutrons and charged particles from the reaction⁵⁸Ni+⁴⁶Ti were measured in coincidence with delayed γ-rays. Six new γ-ray transitions with intensities of 1–10% of the main γ-ray cascade were found, two new states established and firm spin-parity assignments were made to all states below the isomer. The new states were identified as the 4⁺ and 6⁺ members of the proton πg_9/2 ^?2 multiplet.     

Numerische Auswertung der Messdaten eines Neutronendiffraktometers

Ohne Zusammenfassung     

Inhaltsmessung im R3 fester KrÜmmung

Ohne ZusammenfassungDen Manen L.Schläflis und dem Jubilar A.Ostrowski gewidmet