5,762 research outputs found
Approach to a rational rotation number in a piecewise isometric system
We study a parametric family of piecewise rotations of the torus, in the
limit in which the rotation number approaches the rational value 1/4. There is
a region of positive measure where the discontinuity set becomes dense in the
limit; we prove that in this region the area occupied by stable periodic orbits
remains positive. The main device is the construction of an induced map on a
domain with vanishing measure; this map is the product of two involutions, and
each involution preserves all its atoms. Dynamically, the composition of these
involutions represents linking together two sector maps; this dynamical system
features an orderly array of stable periodic orbits having a smooth parameter
dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure
The influence of defects of the fatigue resistance of butt and girth welds in A106B steel
This three-phase study was directed at developing a fitness for service defect acceptance criteria for welds with defect indications. The study focussed on A106 Gr. B steel pipe. The first phase involved a literature search and critical review to develop the preliminary acceptance criteria to the extent permitted by the data. The second phase developed data for flat plate, wall segment, and vessel specimens containing artificial or natural planar or volumetric defects. The final phase developed acceptance criteria from the test data
Dynamic evolution of the source volumes of gradual and impulsive solar flare emissions
This study compares flare source volumes inferred from impulsive hard X-rays and microwaves with those derived from density sensitive soft X-ray line ratios in the O VII spectrum. The data for this study were obtained with the SMM Hard X-Ray Burst Spectrometer, Earth-based radio observatories, and the SOLEX-B spectrometer on the P78-1 satellite. Data were available for the flares of 1980 April 8, 1980 May 9, and 1981 February 26. The hard X-ray/microwave source volume is determined under the assumption that the same electron temperature or power law index characterizes both the source of hard X-rays and the source of microwaves. The O VII line ratios yield the density and volume of the 2 X 10 to the 6th K plasma. For all three flares, the O VII source volume is found to be smallest at the beginning of the flare, near the time when the impulsive hard X-ray/microwave volume reaches its first maximum. At this time, the O VII volume is three to four orders of magnitude smaller than that inferred from the hard X-ray/microwave analysis. Subsequently, the O VII source volume increases by one or two orders of magnitude then remains almost constant until the end of the flare when it apparently increases again
Ethics of Procedure A Discovery-Based Approach to Ex Parte Contacts with Former Employees of a Corporate Adversary
Ethics of Procedure A Discovery-Based Approach to Ex Parte Contacts with Former Employees of a Corporate Adversary
- …