Practical syntheses of [1,3,5]‐triazine dendritic molecules on solid supports

A practical and divergent synthesis of supported [1,3,5]‐triazine dendritic molecules on Wang resin, PEGA resin, SynPhase? Lanterns, and silica gel is described. The alkylamine linkers used allow derivatization with functionality for both synthetic (e.g., supported reagent and scavenger activity) and chemical biology applications. The use of supported intermediates allows differentiation of symmetric linkers without the need for protecting group chemistry. The synthetic route uses inexpensive, readily available starting materials in a straightforward and scaleable strategy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2248–2259, 2006     

SPAR: stochastic programming with adversarial recourse

We consider a general adversarial stochastic optimization model. Our model involves the design of a system that an adversary may subsequently attempt to destroy or degrade. We introduce SPAR, which utilizes mixed-integer programming for the design decision and a Markov decision process (MDP) for the modeling of our adversarial phase.     

Rapid multielemental analysis of Chinese reference soils by laser ablation inductively coupled plasma-source mass spectrometry

Summary Laser ablation inductively coupled plasma-source mass spectrometry has been used to determine thirty elements (Na, Mg, Al, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, As, Rb, Sb, Cs, Ba, La, Ce, Nd, Sm, Eu, Dy, Ho, Yb, Hf, Ta, W, Th, U) in seven Chinese reference soils. The Surrey prototype spectrometer was employed with sample ablation by a free-running ruby laser. Concentrations in the soils (GSS-2 to GSS-8) were calculated from elemental responses and sensitivities derived from another soil in the series, namely GSS-1. Comparisons with previous neutron activation analyses are made. Rapid semiquantitative analyses are proved feasible. About eighty percent of the LA-ICP-MS determined concentrations were within a factor of two of the concentrations measured by INAA, and many were considerably closer than this. Precisions were typically in the range 2–10% RSD, but some were considerably poorer for elements present at trace levels.     

On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications

Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in ℂⁿ and on domains of finite type in ℂ². Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

The determination of indium and thallium in silicate rocks by a combined solvent extraction and spectrochemical technique

A technique has been developed for the determination of In and Tl at very low concentrations in silicate rocks. The iodo-complexes of these elements are extracted from the rock silicate into ethyl cther and the ethereal residues are analysed spectrochemically. The optimum working conditions were established by a study of the variation of percentage extraction as a function of hydrogen iodide normality ; the reproducibility of the spectrochemical procedure was investigated. In and Tl were determined in eight silicate rocks including standard granite G-I and standard diabase W-I. Good agreement was obtained with results of other workers for these two rocks and with the author's previous results. The evidence for a In/Mn coherence in silicate rocks is sufficiently strong to warrant further investigations.