Dynamics of the Douglas-Rachford Method for Ellipses and <Emphasis Type="Italic">p</Emphasis>-Spheres

We expand upon previous work that examined the behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations:that of a line and an ellipse and that of a line together with a p-sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and—seeking a better understanding of the behavior—we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases.     

Nanosized metal deposits on titanium dioxide for augmenting gas-phase toluene photooxidation

The build-up of intermediate species on the surface of TiO₂ during gas-phase toluene (C₇H₈) photodegradation has been observed to deactivate the photocatalyst. Nanosized metallic deposits on the TiO₂ surface may enhance the photocatalytic process and improve photocatalyst performance. In this study, noble (Ag, Au) and platinum group (Pt, Pd, Rh) metals, at a nominal loading of 0.5 at.%, were deposited onto Degussa P25 TiO₂ to enhance photocatalyst performance and inhibit deactivation. Pd, Rh and Au deposits delayed photocatalyst deactivation by a factor of 2, while Pt deposits delayed photocatalyst deactivation by a factor of 20, when compared with neat TiO₂. Ag deposits did not improve photocatalyst activity. Metal deposit performance was related to the work function of each metal, however, the Pt finding suggested that these effects are not governed solely by this aspect, but factors such as deposit characteristics and/or thermal catalytic properties of the metals may be influential.     

Size-dependent oxidation of Pdn (n 13) on alumina/NiAl(110): Correlation with Pd core level binding energies

Small Pd clusters Pd_n (n = 1, 4, 7, 10, 13) deposited on alumina/NiAl(110) at room temperature were examined by X-ray photoelectron spectroscopy (XPS), as-deposited and after exposure to O₂ at temperatures ranging from 100 to 500 K. After O₂ exposure at 100 K, the Pd clusters showed XPS shifts indicative of oxidation. The exception was Pd₄, which did not oxidize under any conditions. The inertness of Pd₄/alumina/NiAl(110) appears to be correlated with a significantly higher-than-expected Pd 3d binding energy, which we attribute to a particularly stable valence shell. None of the clusters examined oxidized during O₂ exposures at 300 K or above, but He⁺ scattering showed that oxygen was bound on the cluster surfaces. Upon heating, all the oxygen associated with these small clusters appeared to spill over and react with the alumina/NiAl(110) support.     

Mathematics teacher training at the State Technical University in Chile

During the fifties and sixties in Chile many mathematics graduates of Pedagogical Institutes became university instructors rather than high school teachers as intended. In the late sixties Masters level programmes began giving more advanced training for university mathematics instructors. A ‘modern’ mathematics curriculum including computer science was introduced in the high schools. The first significant attempt to adapt the training of Chilean high school mathematics teachers to the new academic and social realities was begun in 1976 at the State Technical University with the cooperation of Teachers College, Columbia University, and the support of the Organization of American States.

The four‐year programme leads to Licenciatura (Bachelors) in Mathematics and Computer Education. All courses are taught by faculty members of the Department of Mathematics and Computer Science. The three basic areas of instruction are mathematics, computer science, and mathematics education. Funds provided by the O.A.S. have helped to make possible the development of curricular materials in Spanish, and the acquisition of computing and video tape equipment.     

Variations in T(2)* and fat content of murine brown and white adipose tissues by chemical-shift MRI

Purpose

The purpose was to compare T₂* relaxation times and proton density fat-fraction (PDFF) values between brown (BAT) and white (WAT) adipose tissue in lean and ob/ob mice.

Materials and Methods

A group of lean male mice (n=6) and two groups of ob/ob male mice placed on similar 4-week (n=6) and 8-week (n=8) ad libitum diets were utilized. The animals were imaged at 3 T using a T₂*-corrected chemical-shift-based water–fat magnetic resonance imaging (MRI) method that provides simultaneous estimation of T₂* and PDFF on a voxel-wise basis. Regions of interest were drawn within the interscapular BAT and gonadal WAT depots on co-registered T₂* and PDFF maps. Measurements were assessed using analysis of variance, Bonferroni-adjusted t test for multigroup comparisons and the Tukey post hoc test.

Results

Significant differences (P<.01) in BAT T₂* and PDFF were observed between the lean and ob/ob groups. The ob/ob animals exhibited longer BAT T₂* and greater PDFF than lean animals. However, only BAT PDFF was significantly different (P<.01) between the two ob/ob groups. When comparing BAT to WAT within each group, T₂* and PDFF values were consistently lower in BAT than WAT (P<.01). The difference was most prominent in the lean animals. In both ob/ob groups, BAT exhibited very WAT-like appearances and properties on the MRI images.

Conclusion

T₂* and PDFF are lower in BAT than WAT. This is likely due to variations in tissue composition. The values were consistently lower in lean mice than in ob/ob mice, suggestive of the former's greater demand for BAT thermogenesis and reflective of leptin hormone deficiencies and diminished BAT metabolic activity in the latter.     

Tensor Decomposition With Generalized Lasso Penalties

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features.     

Evaluating continuous chirality measure as a 3D descriptor in chemoinformatics applied to asymmetric catalysis

Continuous Chirality Measure (CCM) is a computational metric by which to quantify the chirality of a compound. In enantioselective catalysis, prior work has postulated that CCM is correlated to selectivity and can be used to understand which structural features dictate catalyst efficacy. Herein, the investigation of CCM as a metric capable of guiding catalyst optimization is explored. Conformer-dependent CCM is also explored. Finally, CCM is used with Sterimol parameters to significantly improve the performance of Random Forest models.     

New Explanation for Ligand Bending in Transition Metal Tris(dithiolate) Complexes

The results of Fenske-Hall molecular orbital calculations are reported for the trigonal prismatic complexes Mo(S(2)C(2)H(2))(3) and Mo(S(2)C(6)H(4))(3). Both complexes exhibit a bend of the S-C-C-S ligand plane away from the S-Mo-S plane. A series of calculations which systematically follow the changes in electronic structure as the bend angle alpha is varied between 0 and 30 degrees indicates that the bend can be attributed to a second order Jahn-Teller distortion. The driving force for this distortion, which allows mixing between a set of ligand pi orbitals and the metal d(z)()()2 orbital, should be greatest for d(0) systems. In these systems the bent geometry leads to the stabilization of the doubly occupied HOMO. The driving force for ligand bending should be lower in systems having more or fewer electrons (e.g. Re(S(2)C(2)Ph(2))(3) or V(S(2)C(2)Ph(2))(3), respectively). While the steric bulk of the dithiolate ligands in the latter complexes may also influence the degree of ligand bending, this is probably a secondary effect.     

Key Word Index for Volume 11

Other Index

Key Word Index for Volume 11