Eigenvalue Boundary Problems for the Dirac Operator

 On a compact Riemannian spin manifold with mean-convex boundary, we analyse the ellipticity and the symmetry of four boundary conditions for the fundamental Dirac operator including the (global) APS condition and a Riemannian version of the (local) MIT bag condition. We show that Friedrich's inequality for the eigenvalues of the Dirac operator on closed spin manifolds holds for the corresponding four eigenvalue boundary problems. More precisely, we prove that, for both the APS and the MIT conditions, the equality cannot be achieved, and for the other two conditions, the equality characterizes respectively half-spheres and domains bounded by minimal hypersurfaces in manifolds carrying non-trivial real Killing spinors. Received: 12 November 2001 / Accepted: 25 June 2002 Published online: 21 October 2002 RID="*" ID="*" Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967 and by European Union FEDER funds     

Development of high-frequency true-linear generator for electrochemical purposes

A new design for a true-linear generator suitable for electrochemical measures is presented. The main component of generation system is an MAX038 chip, a high-frequency relaxation-type oscillator. The design is completed with a digital interface for computer control and an output stage to make signal suitable for cyclic voltammetry experiments. A digital circuit is also included to obtain single sweep signals by isolating one period or a half-period from continuous original output. Performance of presented generator is tested up to 1 MV s(-1) obtaining good stability and linearity.     

Electrochemical reduction of tricarbonyl compounds: Reduction mechanism of alloxan on a mercury electrode

A study has been carried out on the reduction mechanism of alloxan over a DME corresponding to the first two-electron transfer over the pH range 0–12.Polarographic and voltammetric results show the reduction process to be kinetically controlled. Rate and equilibrium constant data for the prior chemical reaction have been evaluated and several reaction mechanisms for different pH zones have been proposed.     

Representation-finite trivial extension algebras

Let A be a finite-dimensional basic connected associative algebra over an algebraically closed field, and $\text{T(A)=A ? DA}$ its trivial extension by its minimal injective cogenerator. We prove that T(A) is representation-finite of Cartan class Δ if and only if A is an iterated tilted algebra of Dynkin class Δ. The proof also yields a construction procedure for iterated tilted algebras of Dynkin type.     

Electron-phonon interaction and current in strong electric fields

Using the Houston-wave approach we investigate the electron-phonon interaction in electric fieldsF which are sufficiently strong to change an electron's Bloch state drastically during the relaxation time τ, but still too weak to support standing electron waves between the band edges. We calculate τ for the low density, high temperature limit and find τ～F ^?1/2. The electric current in the field region of the “hot electrons” between its ohmic rise and its decrease proportional toF ^?1 is determined. Its increase withF ^+1/2 in the limit of relatively low fields agrees with Shockley's result.     

Four-Operator Splitting via a Forward–Backward–Half-Forward Algorithm with Line Search

In this article, we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed method takes advantage of the intrinsic properties of each operator, generalizing the forward–backward–half-forward splitting and the Tseng’s algorithm with line search. At each iteration, our algorithm defines the step size by using a line search in which the monotone-Lipschitzian and the cocoercive operators need only one activation. We also derive a method for solving nonlinearly constrained composite convex optimization problems in real Hilbert spaces. Finally, we implement our algorithm in a nonlinearly constrained least-square problem and we compare its performance with available methods in the literature.

     

Fixed point theorems in new generalized metric spaces

The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi: 10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler–Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.