On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

Remote sensing of the Martian surface

Researchers investigated the physical properties of the Martian surface as inferred from a combination of orbiting and earth-based remote sensing observations and in-situ observations. This approach provides the most detailed and self-consistent view of the global and regional nature of the surface. Results focus on the areas of modeling the diurnal variation of the surface temperature of Mars, incorporating the effects of atmospheric radiation, with implications for the interpretation of surface thermal inertia; modeling the thermal emission from particulate surfaces, with application to observations of the surfaces of the Earth, Moon, and Mars; modeling the reflectance spectrum of Mars in an effort to understand the role of particle size in the difference between the bright and dark regions; and determining the slope properties of different terrestrial surfaces and comparing them with planetary slopes derived from radar observations

Carbohydrates as enantioinduction components in stereoselective catalysis

Carbohydrate derivatives are readily available chiral molecules, yet they are infrequently employed as enantioinduction components in stereoselective catalysis. In this review, synthetic approaches to carbohydrate-based ligands and catalysts are outlined, along with example applications in enantioselective catalysis. A wide range of carbohydrate-based functionality is covered, and key trends and future opportunities are identified

Stereoselective synthesis of glycosides using (salen)Co catalysts as promoters

The use of (salen)Co catalysts as a new class of bench-stable stereoselective glycosylation promoters of trichloroacetimidate glycosyl donors at room temperature is described.</p

Carbohydrate-based N-heterocyclic carbenes for enantioselective catalysis

Versatile syntheses of C2-linked and C2-symmetric carbohydrate-based NHC·HCls from functionalised amino-carbohydrate derivatives are reported. The corresponding Rh complexes were evaluated in asymmetric hydrosilylation of ketones.</p

Fabricating Functionally Graded Materials by Ceramic On-Demand Extrusion with Dynamic Mixing

Ceramic On-Demand Extrusion (CODE) is an extrusion-based additive manufacturing process recently developed for fabricating dense, functional ceramic components. Presented in this paper is a further development of this process focusing on fabrication of functionally graded materials (FGM). A dynamic mixing mechanism was developed for mixing constituent ceramic pastes, and an extrusion control scheme was developed for fabricating specimens with desired material compositions graded in real time. FGM specimens with compositions graded between Al2O3 and ZrO2 were fabricated and ultimately densified by sintering to validate the effectiveness of the CODE process for FGM fabrication. Energy dispersive spectroscopy (EDS) was used to compare final compositions to the original material designs. The specimen’s hardness at different locations along the gradients was examined by micro-indentation tests. The dimensions of sintered specimens were measured, and the effects of material composition gradients on the distortions of sintered FGM specimens were analyze