Spanwise variations in nominally two-dimensional rough-wall boundary layers

Laboratory experiments have been conducted in two separate boundary layer facilities to investigate steady spanwise variations in mean velocity discovered during studies of developing flows over regular arrays of large roughness elements. Regular spanwise variation was found with a steady wavelength, moderated by the growing boundary layer, which was an integer multiple of the repeating unit of roughness. Amplitude variations greater than ±5% in the mean were found over the roughness and greater than ±10% in turbulence quantities. Due to the dominating nature of this phenomena throughout the layer, care should be taken in undertaking local measurements aimed at identifying flow variations caused by roughness heterogeneity.     

Low-degree minimum spanning trees

Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that, under theL _p norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where the maximum degree is minimized. We give the best-known bounds for the maximum MST degree for arbitraryL _p metrics in all dimensions, with a focus on the rectilinear metric in two and three dimensions. We show that for any finite set of points in the rectilinear plane an MST exists with maximum degree of at most 4, and for three-dimensional rectilinear space the maximum possible degree of a minimum-degree MST is either 13 or 14. Gabriel Robins was partially supported by NSF Young Investigator Award MIP-9457412. Jeffrey Salowe was partially supported by NSF Grants MIP-9107717 and CCR-9224789.     

Bioactive diterpenoid containing a reversible "spring-loaded" (E,Z)-dieneone Michael acceptor

Three new briarane diterpenoids, briareolate esters L-N (1-3), have been isolated from a gorgonian Briareum asbestinum. Briareolate esters L (1) and M (2) are the first natural products possessing a 10-membered macrocyclic ring with a (E,Z)-dieneone and exhibit growth inhibition activity against both human embryonic stem cells (BG02) and a pancreatic cancer cell line (BxPC-3). Briareolate ester L (1) was found to contain a "spring-loaded" (E,Z)-dieneone Michael acceptor group that can form a reversible covalent bond to model sulfur-based nucleophiles.     

2' And 3'-ketonucleosides and their arabino and xylo reduction products: Convenient access via selective protection and oxidation of ribonucleosides

A number of 2',5'- or 3',5'-diprotected ribonucleosides and 5'-protected 2'- or 3'-deoxy-β-D-erythro-pentofuranosyl nucleosides have been oxidized to the corresponding 3' or 2'-ketonucleoside derivatives using chromium trioxide/pyridine/acetic anhydride or dimethyl sulfoxide/ acetic anhydride. Reduction of the carbonyl functions with sodium borohydride gave the inverted arabino, xylo, or deoxy-threo isomers as predominant products by attack at the less hindered α-face of the sugar ring. Parallel reductions using sodium borodeuteride corroborated the epimeric ratios by demonstrating that complete oxidation of the original hydroxyl groups had occurred. The deuterium labeling also aided in making NMR spectral assignments.