Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

Mimotopes and Proteome Analyses Using Human Genomic and cDNA Epitope Phage Display

In the post-genomic era, validation of candidate gene targets frequently requires proteinbased strategies. Phage display is a powerful tool to define protein-protein interactions by generating peptide binders against target antigens. Epitope phage display libraries have the potential to enrich coding exon sequences from human genomic loci. We evaluated genomic and cDNA phage display strategies to identify genes in the 5q31 Interleukin gene cluster and to enrich cell surface receptor tyrosine kinase genes from a breast cancer cDNA library. A genomic display library containing 2 × 10 6 clones with exon-sized inserts was selected with antibodies specific for human Interleukin-4 (IL-4) and Interleukin-13. The library was enriched significantly after two selection rounds and DNA sequencing revealed unique clones. One clone matched a cognate IL-4 epitope; however, the majority of clone insert sequences corresponded to E. coli genomic DNA. These bacterial sequences act as ‘mimotopes’ (mimetic sequences of the true epitope), correspond to open reading frames, generate displayed peptides, and compete for binding during phage selection. The specificity of these mimotopes for IL-4 was confirmed by competition ELISA. Other E. coli mimotopes were generated using additional antibodies. Mimotopes for a receptor tyrosine kinase gene were also selected using a breast cancer SKBR-3 cDNA phage display library, screened against an anti-erbB2 monoclonal antibody. Identification of mimotopes in genomic and cDNA phage libraries is essential for phage display-based protein validation assays and two-hybrid phage approaches that examine protein-protein interactions. The predominance of E. coli mimotopes suggests that the E. coli genome may be useful to generate peptide diversity biased towards protein coding sequences

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)

Income Taxes, Sorting, and the Costs of Housing: Evidence from Municipal Boundaries in Switzerland

This paper provides novel evidence on the role of income taxes for residential rents and spatial sorting. Drawing on comprehensive apartment-level data, we identify the effects of tax differentials across municipal boundaries in Switzerland. The boundary discontinuity design (BDD) corrects for unobservable location characteristics such as environmental amenities or the access to public goods and thereby reduces the estimated response of housing prices by one half compared to conventional estimates: we identify an income tax elasticity of rents of about 0.26. We complement this approach with census data on local sociodemographic characteristics and show that about one third of this effect can be traced back to a sorting of high-income households into low-tax municipalities. These findings are robust to a matching approach (MBDD) which compares identical residences on opposite sides of the boundary and a number of further sensitivity checks