The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.
We have carried out molecular-orbital calculations of the four bases of DNA, adenine (A), thymine (T), guanine (G), and cytosine (C), and the dimer dApA formed from a deoxyadenosine by using a phosphate and terminating at the sites of 5 0 and 3 0 . The calculated results for A, T, G, and C are compared with the UPS spectra obtained by using a He II lamp with irradiation at 40.8 eV, and the experimental spectra are found to be generally reproduced by the calculations. We have also examined the alignment of 1.5-mm-length ring-shaped pBR322DNA composed of 4361 bp on Si(1 0 0) substrates with one-dimensional lattices. It is found that pBR322DNA can be observed only in the bottom parts of the one-dimensional lattice, while no appreciable DNA can be observed on the top parts of the lattice. These results suggest that DNA alignment can be controlled by one-dimensional lattices on Si(1 0 0) substrates through capillary action. r
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