Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

A goldstone mode in the Kawasaki-Ising model

The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a quantum extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.     

Multivoice Littlewood-Paley-Meyer wavelets and diagonal dominated pseudodifferential operators

Given a pseudodifferential operator (p) satisfying certain growth and smoothness conditions in momentum space, we construct a wavelet basis ofL ²( ^d ) in which the corresponding matrix is diagonal dominated with arbitrarily small prefactor.     

The adiabatic approximation for quantum spin systems with a spectral gap

Summary We estimate the accuracy of the adiabatic approximation in predicting the time evolution of local observables for an XY quantum magnet with a slowly variable external magnetic field. The system evolves according to the natural Hamiltonian dynamics and the spectral gap produced by the magnetic field is assumed to be large with respect to the term inducing quantum fluctutions. The proof is based on a finite order truncation of a time dependent cluster expansion in inverse powers of the time scale . In the analytic case, we show that the accuracy of this truncated expansion is of order for any >1. If the time dependent perturbation is suddenly switched on at time zero and switched off at time , the accuracy of the adiabatic approximation is proven to be of orderO( ^–1.     

Lineare Oligopeptide. 29. Mitt. IR-Konformations-Analyse von Homo-Oligopeptiden im Festzustand und in Lösung

Ohne Zusammenfassung     

Synthesis,characterization and a thermogravimetric study of copper,cobalt and tin mono- and bis-adducts with ethyleneurea,ethylenethiourea and propyleneurea

This paper describes the synthesis, characterization and a thermogravimetric (t.g.) study of 11 adducts of general formula MCl₂·nL (M = Cu, Co and Sn; n = 1 and 2 for Sn, and 2 for Cu and Co; L = ethyleneurea eu, ethylenethiourea etu, and propyleneurea pu). The i.r. results shows that the eu and pu adducts are coordinated through oxygen, whereas for etu nitrogen is the coordination site. The (C=O) or (C=S) trend is: Cu > Co > Sn. The t.g. curves show that the adducts release ligand molecules in a single mass loss step. As regards considering adducts with the same stoichiometry, the observed thermal stability trend is: etu > pu > eu.     

A unique tautomer of 1‐n‐hexyl‐3‐phenyl‐1H‐pyrazol‐5‐ol

In the title compound, C₁₅H₂₀N₂O, the bond distances and angles are consistent with the presence of the hydroxy tautomer. This tautomer was unambiguously determined by the clear presence of a H atom bonded to oxygen, as well as the total absence of any residual electron density around the N atom in the heterocycle, thus precluding any possibility of desmotropism.     

Low-Cost Potentiometric Sensor for Chloride Measurement in Continuous Industrial Process Control

Recently, the new updates in legislation about drinking water control and human health have increased the demand for novel electrochemical low-cost sensors, such as potentiometric ones. Nowadays, the determination of chloride ion in aqueous solutions has attracted great attention in several fields, from industrial processes to drinking water control. Indeed, chloride plays a crucial role in corrosion, also influencing the final taste of beverages, especially coffee. The main goal is to obtain devices suitable for continuous and real-time analysis. For these reasons, we investigated the possibility to develop an easy, low-cost potentiometric chloride sensor, able to perform analysis in aqueous mediums for long immersion time and reducing the need of periodic calibration. We realized a chloride ion selective electrode made of Ag/AgCl sintered pellet and we tested its response in model solutions compatible with drinking water. The sensor was able to produce a stable, reproducible, and accurate quantification of chloride in 900 s, without the need for a preliminary calibration test. This opens the route to potential applications of this sensor in continuous, in situ, and real time measurement of chloride ions in industrial processes, with a reduced need for periodic maintenance.     

The Small Molecule PPARγ Agonist GL516 Induces Feeding-Stimulatory Effects in Hypothalamus Cells Hypo-E22 and Isolated Hypothalami

PPARγ agonists are implicated in the regulation of diabetes and metabolic syndrome and have therapeutic potential in brain disorders. PPARγ modulates appetite through its central effects, especially on the hypothalamic arcuate nucleus (ARC). Previous studies demonstrated that the small molecule GL516 is a PPARγ agonist able to reduce oxidative stress and apoptosis with a potential neuroprotective role. Herein, we investigated the effects of GL516, in vitro and ex vivo, on the levels of hypothalamic dopamine (DA) and serotonin (5-HT). The gene expressions of neuropeptide Y, CART, AgRP, and POMC, which play master roles in the neuroendocrine regulation of feeding behavior and energy balance, were also evaluated. HypoE22 cells were treated with H₂O₂ (300 μM) for 2 h e 30’ and with different concentrations of GL516 (1 nM-100 µM). The cell viability was evaluated after 24 and 48 h of culturing using the MTT test. DA and 5-HT levels in the HypoE22 cell supernatants were analyzed through HPLC; an ex vivo study on isolated hypothalamic specimens challenged with scalar concentrations of GL516 (1–100 µM) and with pioglitazone (10 µM) was carried out. The gene expressions of CART, NPY, AgRP, and POMC were also determined by a quantitative real-time PCR. The results obtained showed that GL516 was able to reduce DA and 5-HT turnover; moreover, it was effective in stimulating NPY and AgRP gene expressions with a concomitant reduction in CART and POMC gene expressions. These results highlight the capability of GL516 to modulate neuropeptide pathways deeply involved in appetite control suggesting an orexigenic effect. These findings emphasize the potential use of GL516 as a promising candidate for therapeutical applications in neurodegenerative diseases associated with the reduction in food intake and stimulation of catabolic pathways.