Total dissolution of environmental and biological samples by closed-vessel microwave digestion for radiometric analysis

Dry soil, fish-fillet ash, and grass ash were dissolved with a closed-vesselmicrowave oven system and mineral acids. Reagents and dissolution conditionswere varied to ensure total dissolution and recovery of radionuclides. Solventsto dissolve 99.9% of the mass of 3 g samples satisfactorily were 45 ml 14NHF followed by 60 ml 4N HNO₃ saturated with H₃BO₃ for soil, 60 ml 9N HNO₃ followed by 60 ml 14N HF for grass,and 60 ml 9N HNO₃ for fish. The reliability of the dissolutionwas tested with samples from the DOE Quality Assurance Program.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Mantel's theorem for random graphs

For a graph G, denote by t(G) (resp. b(G)) the maximum size of a triangle‐free (resp. bipartite) subgraph of G. Of course for any G, and a classic result of Mantel from 1907 (the first case of Turán's Theorem) says that equality holds for complete graphs. A natural question, first considered by Babai, Simonovits and Spencer about 20 years ago is, when (i.e., for what p = p(n)) is the “Erd?s‐Rényi” random graph G = G(n,p) likely to satisfy t(G) = b(G)? We show that this is true if for a suitable constant C, which is best possible up to the value of C. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 59–72, 2015     

Note on a problem of M. Talagrand

Answering a question of M. Talagrand, we show that there is a fixed L with the following property. For positive integers and , if is the set of subgraphs of K_n containing at least copies of K_k, then there is a set of subgraphs of K_n such that (i) each member of contains a member of and (ii) (where means number of edges). © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 663–668, 2015     

Radiation damage to alkyl chain monolayers on semiconductor substrates investigated by electron spectroscopy

Monolayers of alkyl chains, attached through direct Si-C bonds to Si(111), via phosphonates to GaAs(100) surfaces, or deposited as alkyl-silane monolayers on SiO2, are investigated by ultraviolet and inverse photoemission spectroscopy and X-ray absorption spectroscopy. Exposure to ultraviolet radiation from a He discharge lamp, or to a beam of energetic electrons, leads to significant damage, presumably associated with radiation- or electron-induced H-abstraction leading to carbon-carbon double-bond formation in the alkyl monolayer. The damage results in an overall distortion of the valence spectrum, in the appearance of (occupied) states above the highest occupied molecular orbital of the alkyl molecule, and in a characteristic (unoccupied state) pi resonance at the edge of the carbon absorption peak. These distortions present a serious challenge for the interpretation of the electronic structure of the monolayer system. We show that extrapolation to zero damage at short exposure times eliminates extrinsic features and allows a meaningful extraction of the density of state of the pristine monolayer from spectroscopy measurements.     

Covalently Coupled Immunostimulant Heterodimers

We report increased stimulation of dendritic cells via heterodimers of immunostimulants formed at a discrete molecular distance. Many vaccines present spatially organized agonists to immune cell receptors. These receptors cluster suggesting that signaling is increased by spatial organization and receptor proximity, but this has not been directly tested for multiple, unique receptors. In this study we probe the spatial aspect of immune cell activation using heterodimers of two covalently attached immunostimulants.     

Crystallization of DNA‐Capped Gold Nanoparticles in High‐Concentration,Divalent Salt Environments

The multiparametric nature of nanoparticle self‐assembly makes it challenging to circumvent the instabilities that lead to aggregation and achieve crystallization under extreme conditions. By using non‐base‐pairing DNA as a model ligand instead of the typical base‐pairing design for programmability, long‐range 2D DNA–gold nanoparticle crystals can be obtained at extremely high salt concentrations and in a divalent salt environment. The interparticle spacings in these 2D nanoparticle crystals can be engineered and further tuned based on an empirical model incorporating the parameters of ligand length and ionic strength.