Determination of colloidally-associated polycyclic aromatic hydrocarbons (PAHs) in fresh water using C18 solid phase extraction disks

A new application of reversed-phase octadecyl (C₁₈) solid phase extraction disks has been developed to separate the colloidally-associated polycyclic aromatic hydrocarbons (PAHs) from those that were truly dissolved in the samples of fresh water. A correction for the retention of small amounts of colloidal material on the C₁₈ disks was required, which would have otherwise lead to minor underestimates in the degree of partitioning between the two phases. Using the humic substance Aldrich Humic Acid (AHA) as a model colloid and the 16 PAHs on the US Enrivonmental Protection Agency priority pollutant list, the partitioning coefficients of the PAHs between the colloidal and truly dissolved phases were shown to be proportional to the hydrophobicity of the PAHs, as measured by their octanol water partition coefficients (K_ow). The values for the partition coefficients obtained (cK_doc′) were similar to those previously reported in the literature using alternative methods, confirming that the technique was producing acceptable results. The technique allows the in situ partitioning of PAHs between the truly dissolved and colloidal phases in fresh water bodies to be determined. It will provide an invaluable cross-check of the laboratory-based methods which often require substantial manipulation of the sample and potentially alter the partitioning between the phases.     

The six semifield planes associated with a semifield flock

In 1965 Knuth (J. Algebra 2 (1965) 182) noticed that a finite semifield was determined by a 3-cube array (a_ijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f,g) where f and g are functions from GF(q) to GF(q) with the property that f and g are linear over some subfield and g(x)²+4xf(x) is a non-square for all x∈GF(q)∗, q odd, give rise to certain semifields, one of which is commutative of rank 2 over its middle nucleus, one of which arises from a semifield flock of the quadratic cone, and another that comes from a translation ovoid of Q(4,q). We show that there are in fact six non-isotopic semifields that can be constructed from such a pair of functions, which will give rise to six non-isomorphic semifield planes, unless (f,g) are of linear type or of Dickson-Kantor-Knuth type. These six semifields fall into two sets of three semifields related by Knuth operations.     

Temperaturmessung

Ohne Zusammenfassung     

Recent developments in algebraic combinatorics

We survey three recent developments in algebraic combinatorics. The first is the theory of cluster algebras and the Laurent phenomenon of Sergey Fomin and Andrei Zelevinsky. The second is the construction of toric Schur functions and their application to computing three-point Gromov-Witten invariants, by Alexander Postnikov. The third development is the construction of intersection cohomology for nonrational fans by Paul Bressler and Valery Lunts and its application by Kalle Karu to the torich-vector of a nonrational polytope. We also briefly discuss the “half hard Lefschetz theorem” of Ed Swartz and its application to matroid complexes. Partially supported by NSF grant #DMS-9988459.     

Asymmetric synthesis of 6-(2′,3′,4′,5′,6′-pentafluorophenyl)-δ-lactones via “allyl”boranes: application for the synthesis of fluorinated analog of key pharmacophore of statin drugs

Asymmetric “allyl”boration of pentafluorobenzaldehyde with various α-pinene based “allyl”boranes provides homoallylic alcohols in high de and ee; the alcohols have been converted into δ-lactones via acryloylation, ring-closing metathesis and hydrogenation. Pentafluorophenyl analog of key pharmacophore of statin drugs has been synthesized using diastereoselective epoxidation and regioselective reduction as key steps.     

The Linear Rational Pseudospectral Method with Preassigned Poles

We present a linear rational pseudospectral (collocation) method with preassigned poles for solving boundary value problems. It consists in attaching poles to the trial polynomial so as to make it a rational interpolant. Its convergence is proved by transforming the problem into an associated boundary value problem. Numerical examples demonstrate that the rational pseudospectral method is often more efficient than the polynomial method.     

The interlace polynomial of a graph

Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers.     

Reagent concentration effects in the REM resin solid phase synthesis of tertiary amines

The use of reagent concentration has resulted in increased rates for all stages of the REM resin synthesis of tertiary amines. These increases in rate translate into faster reaction times, higher yields and lower reagent consumption. Of the methods examined, the most successful was the use of perfluorous solvents, either alone or with a small amount of organic co-solvent.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.