On decomposition of continuity

Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.     

Stability testing in an integrated scheme

ISO Guide 35 deals with RM stability issues and scrutinizes the evaluation of stability testing results under the assumption that either there is no trend at all (a rather rare situation), or any observed deterministic change is insignificant and thus can be neglected. However, market demands for reliable reference materials are obviously not limited to stable or at least seemingly stable materials. In many analytical applications, analytes and measurands under consideration are known, or at least suspected, to be unstable on time scales that may vary widely from measurand to measurand. The Federal Institute for Materials Research and Testing (BAM) has developed (and successfully uses) an integrated approach in its certification practice. The approach is based on an initial stability study and subsequent post-certification monitoring. Data evaluation is model-based and takes advantage of all information collected in the stability testing scheme(s). It thus allows one to deal with any kind of instability observed, to assess limiting time intervals at any stress condition in the range tested, to estimate a final expiry date for materials with detected instabilities or the maximum admissible re-testing interval for seemingly stable materials, and to assess maximum admissible stress loads during delivery of the material to the customer. The article describes (and exemplifies) typical study layout, the model selection, and the integrated data assessment.     

Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

Affine-scaling for linear programs with free variables

The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.     

Geometrical method for determining the surface damage threshold for femtosecond laser pulses

A new geometrical method to determine the surface damage threshold for ultrashort pulses is presented. It consists in the formation of a surface damage profile by a movement of the sample across the laser beam focus. A single measurement of the maximum transversal dimension of this damage profile, which depends solely on the laser beam power, is used to calculate the local damage threshold intensity. It is also theoretically shown that the damage in the transverse dimension can be controlled under the diffraction-limited spot.     

Germanium growth on Br-terminated Si(1 0 0)

The consequences of Ge deposition on Br-terminated Si(1 0 0) were studied with scanning tunneling microscopy at ambient temperature after annealing at 650 K. One monolayer of Br was sufficient to prevent the formation of Ge huts beyond the critical thickness of 3 ML. This is possible because Br acts as a surfactant whose presence lowered the diffusivity of Ge adatoms. Hindered mobility was manifest at low coverage through the formation of short Ge chains. Further deposition resulted in the extension and connection of the Ge chains and gave rise to the buildup of incomplete layers. The deposition of 7 ML of Ge resulted in a rough surface characterized by irregularly shaped clusters. A short 800 K anneal desorbed the Br and allowed Ge atoms to reorganize into the more energetically favorable “hut” structures produced by conventional Ge overlayer growth on Si(1 0 0).