Nuclear charge radii and electromagnetic moments of scandium isotopes and isomers in the f7/2 shell

Collinear laser spectroscopy experiments on the ScII transition 3d4s ³D₂→3d4p ³F₃ at λ ≈ 363.1 nm were performed on the ^42–46Sc isotopic chain using an ion guide isotope separator with a cooler–buncher. Isotope and isomer shifts and hyperfine structures of five ground states and two isomers were measured. Preliminary results on the nuclear moments and charge radii changes deduced from these measurements are reported.     

Reconstruction of Convex Bodies from Brightness Functions

Abstract. Algorithms are given for reconstructing an approximation to an unknown convex body from finitely many values of its brightness function, the function giving the volumes of its projections onto hyperplanes. One of these algorithms constructs a convex polytope with less than a prescribed number of facets, while the others do not restrict the number of facets. Convergence of the polytopes to the body is proved under certain essential assumptions including origin symmetry of the body. Also described is an oracle-polynomial-time algorithm for reconstructing an approximation to an origin-symmetric rational convex polytope of fixed and full dimension that is only accessible via its brightness function. Some of the algorithms have been implemented, and sample reconstructions are provided.     

Bijections of #x211D; n onto itself

We characterize affine and continuous maps within the class of bijections of #x211D; ⁿ onto itself by the preservation of various geometric or topological figures. A characterization of similarity maps of Hilbert space is given.Supported in part by a grant from the National Science Foundation.     

A solution to Hammer's X-ray reconstruction problem

We propose algorithms for reconstructing a planar convex body K from possibly noisy measurements of either its parallel X-rays taken in a fixed finite set of directions or its point X-rays taken at a fixed finite set of points, in known situations that guarantee a unique solution when the data is exact. The algorithms construct a convex polygon Pk whose X-rays approximate (in the least squares sense) k equally spaced noisy X-ray measurements in each of the directions or at each of the points.It is shown that these procedures are strongly consistent, meaning that, almost surely, Pk tends to K in the Hausdorff metric as k→∞. This solves, for the first time in the strongest sense, Hammer's X-ray problem published in 1963.     

A model for determining weights of traits in simultaneous multitrait selection

Simultaneous multitrait selection in plant breeding requires knowledge of the relative values, or tradeoffs, of the various traits being considered. An optimization model is developed which will allow quantification of the relative weights present in a breeder's subjective ranking of genotypes, the ranking being based on the apparent relative value of the genotypes. The model is completely general in nature. It allows specification of nonlinear solution functions as well as a linear solution function. It is not specific to any single plant species, nor is it specific to any number or type of traits. While the model is completely general, for purposes of illustration the development of the model is restricted to the linear case. The use of the model in an applied breeding experiment is illustrated using data provided by an experienced maize breeder. The data represent selected and ranked families of genotypes, where the selection and ranking criteria are the relative family performances of three traits considered of economic importance. Relative weights for the three traits are obtained from the initial ranking, and the technique is then used iteratively to demonstrate its usefulness as an interactive procedure.     

Dynamic optical property changes: implications for reflectance feedback control of photocoagulation.

During laser treatment, coagulation affects the optical properties of the tissue. In particular, the formation of a white lesion significantly increases the scattering coefficient. This change in the optical properties in turn affects the laser light distribution in the tissue. The white lesion formed during photocoagulation of the retina has a dynamic effect upon reflection and fluence rate. This problem has been simulated on a model medium consisting of a thin absorbing layer covered with a 1 cm thick layer of albumin. The albumin layer is subdivided into coagulated (white) and uncoagulated (clear) layers. The optical properties of each layer have been determined and these values have been used to model light distribution in the medium. One-dimensional adding-doubling and three-dimensional Monte Carlo methods have provided light distributions in the medium for varying thicknesses of the coagulated albumin. Computed fluence reaching the absorbing layer decreased in the presence of a 275 microns or thicker coagulated layer. The coagulated layer attenuates light because it is highly scattering; however, this scattering also leads to a sub-surface peak in fluence rate at a level higher than the incident fluence. The latter effect outweighed the former for coagulated layer thicknesses less than 275 microns. Computed reflectance of argon laser light from a semi-infinite coagulated region initially increased linearly as a function of thickness. As the coagulation thickness increased beyond 4-5 optical depths, the reflectance approached a constant value, R infinity, at 9 optical depths (2 mm). Experimentally measured total reflectance is shown to be an inadequate indicator of the thickness of a lesion (finite coagulated volume); however, central reflectance from a lesion measured with a CCD camera confirmed the computed trends. These results provide a theoretical foundation for control of lesion thickness using reflectance images.     

Untersuchung von Kartoffeln, Gerste und Malz

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