Generally the density of the environment is important for the formation and evolution of galaxies: bright elliptical galaxies reside in the centers of galaxy clusters, whereas late type galaxies preferentially populate small groups, filaments or the outskirts of rich clusters of galaxies. Furthermore, fainter galaxies define smaller voids than bright galaxies. Our investigation of void catalogues in the Northern Local Void region shows that large voids are interlaced by systems of faint galaxies dividing them into smaller subvoids (Lindner et al., 1995). This void hierarchy is an important property of the Large Scale Structure in the nearby Universe and can help to solve problems concerning the distribution of dwarf galaxies and BCDGs.

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It is shown, that in a Hubbard chain modified by coupling to the lattice solitons e x i s w h e y are accompanied by solitary lattice distortions. The non-linearity is caused by the electron correlation as well as by the electron-phonon interaction.Es wird gezeigt, daS in ciner Hubbardkette, die durch Kopplung an das Gitter modifiziert ist, Solitonen existieren, die von solitaren Gitterstorungen begleitet sind. Die Nichtlinearitiit wird sowohl durch die Elektronenkorrelation als auch durch die Elektron-Phonon-Wechselwirkung verarsacht.

(b) From the existence of double solutions of the NBel temperature in the Hubbard model for nearest neighbour overlap and simple cubic lattice in the framework of the Hartree-Fock approximation as well as within the unified theory of Moriya and Hasegawa i t follows that i t is necessary to conclude further magnetic (commensurable and incommensurable) phases in the magnetic phase diagram. The investigation is restricted t o magnetic long-range order.Aus der Existenz von Doppellosungen fur die N6e1-Temperatur im Hubbard-Mode11 fur einfachkubisches Gitter bei Berucksichtigung nachster Nachbarn sowohl in Hartree-Pock-Approximation als auch innerhalb der Theorie von Moriya und Hasegawa folgt, dafl es notwendig ist, weitere magnetische (kommensurable und inkommensurable) Phasen in das magnetische Phasendiagramm einzuschliefien. Die Untersuchungen werden auf lang-reichweitige magnetische Ordnung beschrankt.

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