Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.     

Molecular Design Principles for Near‐Infrared Absorbing and Emitting Indolizine Dyes

Desirable components for dye‐sensitzed solar cell (DSC) sensitizers and fluorescent imaging dyes include strong donating building blocks coupled with well‐balanced acceptor functionalities for absorption beyond the visible range. We have evaluated the effects of increasing acceptor strengths and incorporation of dye morphology controlling groups on molar absorptivity and absorption breadth with indolizine donor‐based dyes. Indolizine‐based D –A and D –π–A sensitizers incorporating bis‐rhodanine, tricyanofuran (TCF), and cyanoacrylic acid functionalities were analyzed for performance in DSC devices. The TCF derivatives were also evaluated as near‐infrared (NIR)‐emissive materials with the AH25 emissions extending past 1000 nm.     

Generating and routing light-bullets using slab waveguide arrays

Light-bullet routing and control is theoretically demonstrated in a slab waveguide architecture using a fully addressable electronic current injection mechanism for gain control. By exploiting gain mediated interactions between bullets, photonic NAND and NOR logic gates are produced on the same chip design. The robustness, simplicity, and control offered by light-bullets in slab waveguide architectures suggest that such devices should be seriously considered as candidates for technological development.

     

Seasonal Variations in the Subsurface Ultraviolet‐B on an Inshore Pacific Coral Reef Ecosystem

Fringing coral reefs provide a unique opportunity to study shallow aquatic ecosystems. A fringing coral reef system located in close proximity to a developed region was considered in this study. In such an environment, the rate of decay of dissolved organic matter is high and the penetration of higher energy ultraviolet‐B (UVB) extends a greater influence on species diversity, particularly upon shallow benthic communities. Results from a 9 month subsurface UVB exposure measurement campaign performed at a site located on the southern Queensland coast (Hervey Bay, 25°S) are presented in this research. For this, a novel dosimetric technique was utilized to measure long‐term subsurface UVB exposures. The resultant data set includes exposure measurements made during the significant La Niña event of late 2010 which resulted in unprecedented high sea surface temperatures and severe flooding across eastern Australia, impacting upon the lagoon regions of the Great Barrier Reef and Queensland's southern estuaries, including the study site. The influence of season, diurnal tidal variation, cloud cover and solar zenith angle were analyzed over the campaign period. Mean minimum daylight water depth was found to be the most significant factor influencing subsurface UVB.     

Divergent reactivity of allene-containing α-diazoesters using Cu and Rh catalysis

A versatile intramolecular reaction of allene-containing diazomalonates that exhibits excellent chemoselectivity for either allenic C–H insertion or cyclopropanation is demonstrated. The identity of the product depends on the transition metal catalyst that is employed for the reaction. Rh catalysts promote exclusive C–H insertion with good diastereoselectivity for the trans product, while Cu catalysis enables intramolecular cyclopropanation to yield methylenecyclopropanes with moderate to good E:Z ratios.     

Neighboring Group Participation in Glycosylation Reactions by 2,6-Disubstituted 2-O-Benzoyl groups: A Mechanistic Investigation

Variable yields and glycosylation stereoselectivity were obtained for NIS/TfOH-medi- ated reaction of 4-methoxyphenyl 2,4,6-tetra-O-acetyl-β-D-galactopyranoside and thiogalactosides bearing acetyl, benzoyl, 2,6-dimethoxylbenzoyl, 2,4,6-trimethylbenzoyl, or 2,6-dichlorobenzoyl groups at the 2-positions and acetyl at the remainder. X-ray structures of 4-methylphenyl 2,3,4,6-tetra-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyr anoside and 4-methylphenyl 3,4-O-isopropylidene-2,6-di-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyranoside revealed slightly distorted ⁴ C ₁ chair conformations. Variable temperature NMR revealed that activation of 4-methylphenyl 2,3,4,6-tetra-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyranoside afforded only dioxolenium ion, whereas 4-methylphenyl 3,4,6-tri-O-acetyl-2-O-(2,4,6-trimethylbenzoyl)-1-thio-β-D-galactopyranoside gave a 1:1 mixture of dioxolenium ion and glycosyl triflate. However, the reaction intermediates formed from these deactivated donors do not influence the glycosylation stereoselectivity; instead, it is influenced by steric and electronic interactions at the transition states.     

Borane Adducts of Aromatic Phosphorus Heterocycles: Synthesis,Crystallographic Characterization and Reactivity of a Phosphinine-B(C6F5)3 Lewis Pair

A phosphinine-borane adduct of a Me₃Si-functionalized phosphinine and the Lewis acid B(C₆F₅)₃ has been synthesized and characterized crystallographically for the first time. The reaction strongly depends on the nature of the substituents in the α-position of the phosphorus heterocycle. In contrast, the reaction of B₂H₆ with various substituted phosphinines leads to an equilibrium between the starting materials and the phosphinine–borane adducts that is determined by the Lewis basicity of the phosphinine. The novel phosphinine borane adduct ( 6 -B(C₆F₅)₃) shows rapid and facile insertion and [4+2] cycloaddition reactivity towards phenylacetylene. A hitherto unknown dihydro-1-phosphabarrelene is formed with styrene. The reaction with an ester provides a new, facile and selective route to 1-R-phosphininium salts. These salts then undergo a [4+2] cycloaddition in the presence of Me₃Si−C≡CH and styrene to cleanly form unprecedented derivatives of 1-R-phosphabarrelenium salts.