Scattering relations for point‐source excitation in chiral media

A spherical electromagnetic wave propagating in a chiral medium is scattered by a bounded chiral obstacle which can have any of the usual properties. Reciprocity and general scattering theorems, relating the scattered fields due to scattering of waves from a point source put in any two different locations are established. Applying the general scattering theorem for appropriate locations and polarizations of the point source we prove an associated forward scattering theorem. Mixed scattering relations, relating the scattered fields due to a plane wave and the far‐field patterns due to a spherical wave, are also established. Copyright © 2005 John Wiley & Sons, Ltd.     

Solid-phase microextraction–capillary gas chromatography combined with microwave-induced plasma atomic-emission spectrometry for selenite determination

The use of solid-phase microextraction (SPME) with gas chromatography coupled to microwave-induced plasma atomic-emission detection (GC–MIP-AED) is described for selenite [Se(IV)] speciation. Aqueous standards were derivatised with sodium tetraethyl- or tetrapropylborate and extracted by SPME. Headspace extraction of the ethyl and propyl derivatives was studied. Relevant experimental conditions were optimised, including conditions for derivatisation and extraction and those of gas chromatographic analysis. The limits of detection achieved for headspace sampling of derivatised Se(IV) were in the low ng mL^–1 range for both ethylation and propylation. When the method was applied to analysis of selenite in selenised yeast reference material results were in good agreement with the indicated values.     

Solvation and Ion-Pairing Effects of Choline Acetate Electrolyte in Protic and Aprotic Solvents Studied by NMR Titrations

Choline-based electrolytes have been proposed as environmentally friendly and low-cost alternatives for secondary zinc air batteries. Choline acetate [Ch]⁺[OAc]⁻ in protic (D₂O) and aprotic (DMSO-d₆) solvents has been studied by means of concentration-dependent ¹H NMR, viscosity, and density measurements. The viscosities have been calculated on the basis of the Jones-Dole equation and showed that the dominant contribution originates from short-range ion-solvent interactions. Site-specific association affinities were assigned from NMR chemical shift titrations. In DMSO-d₆, the hydroxyl group of choline was found to have the smallest dissociation constant followed by the methyl group of acetate. The corresponding Gibbs energies at low concentration were found to be in agreement with a solvent-separated ion pair (2SIP) configuration, whereas at concentrations above 300 mM, a solvent-shared ion pair (SIP) configuration was assigned. For [Ch]⁺[OAc]⁻ in D₂O, association effects were found to be weaker, attributed to the high dielectric constant of the solvent. On time scales on the order of 100 ms, NMR linewidth perturbations indicated a change in the local rotational dynamics of the ions, attributed to short-range cation-solvent interactions and not to solvent viscosity. At 184 mM, 40 % of the cations in DMSO-d₆ and 10 % in D₂O were found to exhibit short-range interactions, as indicated by the linewidth perturbations. It was found that at about 300 mM, the ions in DMSO-d₆ exhibit a transition from free to collective translational dynamics on time scales on the order of 400 ms. In DMSO-d₆, both ions were found to be almost equally solvated, whereas in D₂O solvation of acetate was stronger, as indicated by the obtained effective hydrodynamic radii. For [Ch]⁺[OAc]⁻ in DMSO-d₆, the results suggest a solvent-shared ion association with weak H-bonding interactions for concentrations between 0.3–1 M. Overall, the extent of ion association in solvents such as DMSO is not expected to significantly limit charge transport and hinder the performance of choline-based electrolytes.     

Practical algorithm substitution attack on extractable signatures

Designs, Codes and Cryptography - An algorithm substitution attack (ASA) can undermine the security of cryptographic primitives by subverting the original implementation. An ASA succeeds when it...     

Spectra of Some Interesting Combinatorial Matrices Related to Oriented Spanning Trees on a Directed Graph

The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H _n ) follows, where H _n stands for the complete directed graph on n vertices without loops.     

Generalized Catalan Numbers, Weyl Groups and Arrangements of Hyperplanes

For an irreducible, crystallographic root system in a Euclideanspace V and a positive integer m, the arrangement of hyperplanesin V given by the affine equations (, x) = k, for and k =0, 1, ..., m, is denoted here by . The characteristic polynomial of is related in the paper to that of the Coxeter arrangement A(corresponding to m = 0), and the number of regions into whichthe fundamental chamber of A is dissected by the hyperplanesof is deduced to be equal to the product , where e₁,e₂, ..., e_l are the exponents of and h is the Coxeter number.A similar formula for the number of bounded regions follows.Applications to the enumeration of antichains in the root posetof are included. 2000 Mathematics Subject Classification 20F55(primary), 05A15, 52C35 (secondary).     

Traces and idempotents in group algebras

Let G be a group and E an idempotent matrix with entries in the complex group algebra C G. In this paper, we study arithmetic properties of the coefficients r _E (g), gG, of the Hattori-Stallings rank r _E of E. Bass proved in [2] that the r _E (g)s are algebraic numbers. Following Zaleskii, we proceed by reduction to positive characteristic and give an alternative proof of that assertion, while obtaining at the same time an upper bound for the degree of the minimum polynomial of r _E (g) over Q.     

Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes

Let Φ be a finite root system of rank n and let m be a nonnegative integer. The generalized cluster complex Δ^m(Φ) was introduced by S. Fomin and N. Reading. It was conjectured by these authors that Δ^m(Φ) is shellable and by V. Reiner that it is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. These statements are proved in this paper. Analogous statements are shown to hold for the positive part Δ₊^m(Φ) of Δ^m(Φ). An explicit homotopy equivalence is given between Δ₊^m(Φ) and the poset of generalized noncrossing partitions, associated to the pair (Φ, m) by D. Armstrong.