Stable Subnorms II

In this paper we continue our study of stability properties of subnorms on subsets of finite-dimensional, power-associative algebras over the real or the complex numbers.     

The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption

In the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation ?Δu + g(x, u) = 0 in a smooth domain Ω ? ?^N, for a general class of positive nonlinearities. This class includes every space independent, monotone increasing g which satisfies the Keller‐Osserman condition as well as degenerate nonlinearities g_α,q of the form g_α,q (x, u) = d(x, ?Ω)^α |u|^q?1 u, with α > ?2 and q > 1. The boundary trace is given by a positive regular Borel measure which may blow up on compact sets. In the second part we concentrate on the family of nonlinearities {g_α,q}, determine the critical value of the exponent q (for fixed α > ?2) and discuss (a) positive solutions with an isolated singularity, for subcritical nonlinearities and (b) the boundary value problem for ?Δu + g_α,q (x, u) = 0 with boundary data given by a positive regular Borel measure (possibly unbounded). We show that, in the subcritical case, the problem possesses a unique solution for every such measure. © 2003 Wiley Periodicals, Inc.     

On queueing delays of dispersed messages

We study the message queueing delays in a node of a communication system, where a message consists of a block of consecutive packets. The message delay is defined as the time elapsing between the arrival epoch of the first packet of the message to the system until after the transmission of the last packet of that message is completed. We distinguish between two types of message generation processes. The message can be generated as abatch or it can bedispersed over time. In this paper we focus on the dispersed generation model. The main difficulty in the analysis is due to the correlation between the system states observed by different packets of the same message. This paper introduces a new technique to analyze the message delay in such systems for different arrival models and different number of sessions. For anM/M/1 system with variable size messages and for the bursty traffic model, we obtain an explicit expression for the Laplace-Stieltjes transform (LST) of the message delay. Derivations are also provided for anM/G/1 system, for multiple session systems and for fixed message sizes. We show that the correlation has a strong effect on the performance of the system, and that the commonly usedindependence assumption, i.e., the assumption that the delays of packets are independent from packet to packet, can lead to wrong conclusions.     

Ion survival probabilities for 3 keV Ar+ scattering from La,Yb, and chemisorbed H2, O2, and H2O on La surfaces

TOF spectra of scattered primary and surface recoiled neutrals and ions for 3 keV Ar⁺ bombardment of clean La and Yb and H₂, O₂, and H₂O saturated La surfaces are presented. The spectra are analyzed in terms of single (SS) and multiple (MS) scattering of the primary ions and surface recoiling (SR) of adsorbate atoms. Measurement of spectra of neutrals + ions and neutrals alone allows determination of scattered ion fractions Y. The Y values for the SS event are high for clean La (37%) and lower for adsorbate covered La (32% for H₂, 13% for O₂, and 8% for H₂O); Yb exhibits a similar behavior, i.e. 16% for clean Yb and 5% for O₂ + H₂O covered Yb. Photon emission accompanying the scattering collision has been observed from clean La and Yb and adsorbate covered La. A preferential inelastic energy loss of 15 ± 3 eV for the SS event has been observed for scattered neutrals as opposed to ions for La and H₂ saturated La at 135°. These results are interpreted within the models for Auger and resonant electronic charge exchange transitions during approach or departure of an ion with a surface and the electron promotions occuring during close atomic encounters where the electron shells are interpenetrating.     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.