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.     

In search of photon’s elementary axial magnetostatic field

 Experimental investigations of the photon’s B ⁽³⁾-field (third longitudinal polarization) are reported. The existence of an “axial magnetostatic field of photon” has been predicted in B _π or B ⁽³⁾-theory as the fundamental property of the circularly polarized light, and reported in numerous papers and monographs. High-sensitivity detection has been employed in photomagnetic induction, Faraday, and inverse Faraday effects (IFE) originating from such a field. The results of all three experiments clearly disprove the claims of B _π-theory. Putting together these results and theoretical calculations in perspective, it is concluded that such fields are non-existent. Received: 25 January 1996 / Revised version: 24 May 1996     

Cycles on curves over global fields of positive characteristic

Let be a global field of positive characteristic, and let be a smooth projective curve. We study the zero-dimensional cycle group and the one-dimensional cycle group , addressing the conjecture that is torsion and is finitely generated. The main idea is to use Abhyankar's Theorem on resolution of singularities to relate the study of these cycle groups to that of the -groups of a certain smooth projective surface over a finite field.

     

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.     

Mechanism and substrate stereochemistry of 2-amino-3-oxobutyrate CoA ligase: implications for 5-aminolevulinate synthase and related enzymes

The condensation process catalysed by 2-amino-3-oxobutyrate CoA ligase (KBL; also known as 2-amino-3-ketobutyrate ligase) involves the loss of the pro-R hydrogen atom of glycine and occurs with the inversion of stereochemistry; a similar scenario is envisaged for the condensation step of other alpha-oxoamine synthases.     

Laser gas-assisted processing of carbon coated and TiC embedded Ti-6Al-4V alloy surface

Laser gas-assisted treatment of Ti-6Al-4V alloy surface is carried out. The alloy surface is initially coated by a carbon layer, in which the TiC particles are embedded prior to laser processing of the surface. The carbon coating with the presence of TiC particles on the workpiece surface is expected to result in carbonitride compound in the surface vicinity after the laser treatment process. Optical and scanning electron microscopes are used to examine the morphological and the metallurgical changes in the laser treated layer. The residual stress formed in the surface region after the laser treatment process is critical for the practical applications of the resulting surface. Therefore, the residual stress formed in the laser treated region is predicted from the analytically equation. The X-ray diffraction technique is incorporated to obtain the residual stress formed in the surface region. It is found that the residual stress predicted agrees with the X-ray diffraction data. The dense structures consisting of TiC_xN_1−x, TiN_x, Ti₂N, and TiC compounds are formed in the surface region of the treated layer. This, in turn, significantly increases the microhardness at the surface.     

Inverse problems for quasi-variational inequalities

In this short note, our aim is to investigate the inverse problem of parameter identification in quasi-variational inequalities. We develop an abstract nonsmooth regularization approach that subsumes the total variation regularization and permits the identification of discontinuous parameters. We study the inverse problem in an optimization setting using the output-least squares formulation. We prove the existence of a global minimizer and give convergence results for the considered optimization problem. We also discretize the identification problem for quasi-variational inequalities and provide the convergence analysis for the discrete problem. We give an application to the gradient obstacle problem.     

DLTS and in situ C–V analysis of trap parameters in swift 50 MeV Li3+ ion-irradiated Ni/SiO2/Si MOS capacitors

Ni/SiO₂/Si MOS structures were fabricated on n-type Si wafers and were irradiated with 50 MeV Li³⁺ ions with fluences ranging from 1×10¹⁰ to 1×10¹² ions/cm². High frequency C–V characteristics are studied in situ to estimate the build-up of fixed and oxide charges. The nature of the charge build-up with ion fluence is analyzed. Defect levels in bulk Si and its properties such as activation energy, capture cross-section, trap concentration and carrier lifetimes are studied using deep-level transient spectroscopy. Electron traps with energies ranging from 0.069 to 0.523 eV are observed in Li ion-irradiated devices. The dependence of series resistance, substrate doping and accumulation capacitance on Li ion fluence are clearly explained. The study of dielectric properties (tan δ and quality factor) confirms the degradation of the oxide layer to a greater extent due to ion irradiation.     

Reproducing-kernel-based splines for the regularization of the inverse ellipsoidal gravimetric problem

To solve the inverse gravimetric problem, i.e. to reconstruct the Earth's mass density distribution by using the gravitational potential, we introduce a spline interpolation method for the ellipsoidal Earth model, where the ellipsoid has a rotational symmetry. This problem is ill-posed in the sense of Hadamard as the solution may not exist, it is not unique and it is not stable. Since the anharmonic part (orthogonal complement) of the density function produces a zero potential, we restrict our attention only to reconstruct the harmonic part of the density function by using the gravitational potential. This spline interpolation method gives the existence and uniqueness of the unknown solution. Moreover, this method represents a regularization, i.e. every spline continuously depends on the given gravitational potential. These splines are also combined with a multiresolution concept, i.e. we get closer and closer to the unknown solution by increasing the scale and adding more and more data at each step.     

Local minimizers versus X-local minimizers

An important property known, among other cases, for W ^1,p (Ω) versus ${C^1(\overline{\Omega})}$ -local minimizers of certain functions is extended to the general situation of local minimizers of a functional I on a Banach space Y versus X-local minimizers of I provided X is a Banach space continuously and densely embedded in Y.