Ladder operators for subtle hidden shape invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.Comment: 9 pages, based on the talk given at International Conference Progress in Supersymmetric Quantum Mechanics (PSQM03), Valladolid, Spain, 15-19 July, 2003, to appear in a Special Issue of J. Phys. A: Math. Ge

Generalized Ladder Operators for Shape-invariant Potentials

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.Comment: in Revte

Analysis of compound heterozygotes reveals that the mouse floxed Pax6 tm1Ued allele produces abnormal eye phenotypes

Analysis of abnormal phenotypes produced by different types of mutations has been crucial for our understanding of gene function. Some floxed alleles that retain a neomycin-resistance selection cassette (neo cassette) are not equivalent to wild-type alleles and provide useful experimental resources. Pax6 is an important developmental gene and the aim of this study was to determine whether the floxed Pax6(tm1Ued) (Pax6(fl)) allele, which has a retained neo cassette, produced any abnormal eye phenotypes that would imply that it differs from the wild-type allele. Homozygous Pax6(fl/fl) and heterozygous Pax6(fl/+) mice had no overt qualitative eye abnormalities but morphometric analysis showed that Pax6(fl/fl) corneas tended be thicker and smaller in diameter. To aid identification of weak effects, we produced compound heterozygotes with the Pax6(Sey-Neu) (Pax6(−)) null allele. Pax6(fl/−) compound heterozygotes had more severe eye abnormalities than Pax6(+/−) heterozygotes, implying that Pax6(fl) differs from the wild-type Pax6(+) allele. Immunohistochemistry showed that the Pax6(fl/−) corneal epithelium was positive for keratin 19 and negative for keratin 12, indicating that it was abnormally differentiated. This Pax6(fl) allele provides a useful addition to the existing Pax6 allelic series and this study demonstrates the utility of using compound heterozygotes with null alleles to unmask cryptic effects of floxed alleles. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11248-016-9962-4) contains supplementary material, which is available to authorized users

Targeted Deletion of Kcne2 Causes Gastritis Cystica Profunda and Gastric Neoplasia

Gastric cancer is the second leading cause of cancer death worldwide. Predisposing factors include achlorhydria, Helicobacter pylori infection, oxyntic atrophy and TFF2-expressing metaplasia. In parietal cells, apical potassium channels comprising the KCNQ1 α subunit and the KCNE2 β subunit provide a K+ efflux current to facilitate gastric acid secretion by the apical H+K+ATPase. Accordingly, genetic deletion of murine Kcnq1 or Kcne2 impairs gastric acid secretion. Other evidence has suggested a role for KCNE2 in human gastric cancer cell proliferation, independent of its role in gastric acidification. Here, we demonstrate that 1-year-old Kcne2−/− mice in a pathogen-free environment all exhibit a severe gastric preneoplastic phenotype comprising gastritis cystica profunda, 6-fold increased stomach mass, increased Ki67 and nuclear Cyclin D1 expression, and TFF2- and cytokeratin 7-expressing metaplasia. Some Kcne2−/−mice also exhibited pyloric polypoid adenomas extending into the duodenum, and neoplastic invasion of thin walled vessels in the sub-mucosa. Finally, analysis of human gastric cancer tissue indicated reduced parietal cell KCNE2 expression. Together with previous findings, the results suggest KCNE2 disruption as a possible risk factor for gastric neoplasia

Disruption of the potassium channel regulatory subunit Kcne2 causes iron-deficient anemia

Iron homeostasis is a dynamic process that is tightly controlled to balance iron uptake, storage, and export. Reduction of dietary iron from the ferric to the ferrous form is required for uptake by solute carrier family 11 (proton-coupled divalent metal ion transporters), member 2 (Slc11a2) into the enterocytes. Both processes are proton dependent and have led to the suggestion of the importance of acidic gastric pH for the absorption of dietary iron. Potassium voltage-gated channel subfamily E, member 2 (KCNE2), in combination with potassium voltage-gated channel, KQT-like subfamily, member 1 (KCNQ1), form a gastric potassium channel essential for gastric acidification. Deficiency of either Kcne2 or Kcnq1 results in achlorhydia, gastric hyperplasia, and neoplasia, but the impact on iron absorption has not, to our knowledge, been investigated. Here we report that Kcne2-deficient mice, in addition to the previously reported phenotypes, also present with iron-deficient anemia. Interestingly, impaired function of KCNQ1 results in iron-deficient anemia in Jervell and Lange-Nielsen syndrome patients. We speculate that impaired function of KCNE2 could result in the same clinical phenotype

Quantitative feedback control of multiple input single output systems

This paper presents a robust feedback control solution for systems with multiple manipulated inputs and a single measurable output. A structure of parallel controllers achieves robust stability and robust disturbance rejection. Each controller uses the least possible amount of feedback at each frequency. The controller design is carried out in the Quantitative Feedback Theory framework. The method pursues a smart load sharing along the frequency spectrum, where each branch must either collaborate in the control task or be inhibited at each frequency. This reduces useless fatigue and saturation risk of actuators. Different examples illustrate the ability to deal with complex control problems that current MISO methodologies cannot solve. Main control challenges arise due to the uncertainty of plant and disturbance models and when a fast-slow hierarchy of plants cannot be uniquely established. © 2014 Javier Rico-Azagra et al