Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Condensation of unsaturated cyclic sulfones with aldehydes

The reactivity of the 2(5) positions of dihydrothiophene dioxide has been studied. Their condensation with aldehydes leads to the formation of 2(5)-substituted derivatives containing a conjugated system of double bonds.     

Diskrete R?ntgenkleinwinkelstreuung durch weichgemachtes Polyvinylchlorid

Ohne Zusammenfassung     

Structure and phase transitions in poly[bis-(2,2,3,3-tetrafluoropropoxy) phosphazene]

The structure and phase transitions in poly[bis-(2,2,3,3-tetrafluoropropoxy)phosphazene] have been studied by differential scanning calorimetry (DSC) and x-ray diffraction. Two crystalline phases and one mesomorphic phase are found, denoted I, II, and III, respectively. These phases convert reversibly one into the other on heating and cooling. The Phase I–Phase II transition occurs in a temperature range from 5 to 30°C whereas the Phase II mesophase (Phase III) transition proceeds above 80°C. Heats of transitions are measured to be about 29.0 J/g and 3.6 J/g, respectively. Crystalline Phase I is characterized by a monoclinic unit cell with the parameters: α = 24.4 Å, b = 9.96 Å, c = 4.96 Å, γ = 123°. The axes of both chains, traversing the unit cell, are directed along the “c” axis, the main chains having cis-trans conformation. Phase I is the common crystalline structure for the main chain and side chains. The structure of Phase II is controlled mainly by packing of the side chains. Transition of Phase II into mesomorphic Phase III is accompanied with distortion of packing of the side chains. Only regular packing of the main chains of macromolecules in the plane perpendicular to their axes exists in Phase III. Mesomorphic phase III is stable up to the degradation temperature of the polymer. A significant effect of stress on the Phase II–III transition in oriented samples was found.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.