New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

Lysyl oxidase ( Lox ) maps between Grl-1 and Adrb-2 on mouse Chromosome 18

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47002/1/335_2004_Article_BF00352234.pd

Regulation of the Egr-1 gene by tumor necrosis factor and interferons in primary human fibroblasts

Journal of Biological Chemistry26721345-1349JBCH

Preeclampsia: a renal perspective.

Preeclampsia: A renal perspective. Preeclampsia is a syndrome that affects 5% of all pregnancies, producing substantial maternal and perinatal morbidity and mortality. The aim of this review is to summarize our current understanding of the pathogenesis of preeclampsia with special emphasis on the recent discovery that circulating anti-angiogenic proteins of placental origin may play an important role in the pathogenesis of proteinuria and hypertension of preeclampsia