On a characterization of irreducibility of a non-negative matrix

Let A denote an n×n matrix with all its elements real and non-negative, and let r_i be the sum of the elements in the ith row of A, i=1,…,n. Let B=A?D(r₁,…,r_n), where D(r₁,…,r_n) is the diagonal matrix with r_i at the position (i,i). Then it is proved that A is irreducible if and only if rank B=n?1 and the null space of B^T contains a vector d whose entries are all non-null.     

Equilibrium behaviour of exchange of [Coen3]3+ on vermiculite

Summary The cation exchange data of tris ethylene diamine cobaltic ion on H-vermiculite fit in with theLangmuir equation. The exchange of [Coen₃]³⁺ by different cations are in the order: Li < Na < NH₄ < K < Rb < H < Cs for the monovalent, Mg Ca < Ba for the bivalent and (C₂H₅)₄N < (CH₃)₄N CTA < CP for monovalent organic ions. Quaternary cations such as (C₂H₅)₄N⁺ exchange less than (CH₃)₄N⁺. This may be ascribed to the larger size of the former and also to the limitedc-axis expansion of vermiculite. By use of the equation ofKielland, thermodynamic equilibrium constants and standardGibbs free energy change have been evaluated. The plots of log (selectivity coefficient) vs. hydrated ionic radius and the reciprocal of theDebye Hückel parametera ⁰, suggest that the parametera ⁰ rather than the hydrated ionic radius may be found to correlate with the relative affinities of univalent cations for the vermiculite surface.     

Aqueous polymerization on clay surfaces. III. The polymerization of methyl methacrylate by montmorillonite/thiourea initiating system

Initiation of polymerization of methyl methacrylate with redox system montmorillonite (with lattice Fe³⁺)–thiourea has been achieved. The rates are dependent on both clay mineral and thiourea. Amidosulfenyl radicals are believed to initiate the polymerization on the clay surface. The polymerization produced nonextractable clay–polymer adduct up to an extent of 70 wt %. The pH of the medium (in the acidic range) did not affect the polymerization rate.     

In-silico screening of high production volume chemicals for mutagenicity using the MCASE QSAR expert system

Computational screening is suggested as a way to set priorities for further testing of high production volume (HPV) chemicals for mutagenicity and other toxic endpoints. Results are presented for batch screening of 2484 HPV chemicals to predict their mutagenicity in Salmonella typhimurium (Ames test). The chemicals were tested against 15 databases for Salmonella strains TA100, TA1535, TA1537, TA97 and TA98, both with metabolic activation (using rat liver and hamster liver S9 mix test) and without metabolic activation. Of the 2484 chemicals, 1868 are predicted to be completely nonmutagenic in all of the 15 data modules and 39 chemicals were found to contain structural fragments outside the knowledge of the expert system and therefore suggested for further evaluation. The remaining 616 chemicals were found to contain different biophores (structural alerts) believed to be linked to mutagenicity. The chemicals were ranked indescending order according to their predicted mutagenic potential and the first 100 chemicals with highest mutagenicity scores are presented. The screening result offers hope that rapid and inexpensive computational methods can aid in prioritizing the testing of HPV chemicals, save time and animals and help to avoid needless expense.     

Alkaloids of Glycosmis arborea—III Structure of arborinine

Arborinine is identical with the 2,3-dimethoxy-1-hydroxy-10-methylacridone of Hughes et al.     

On a fast and accurate method for computing Fourier transforms

In this paper, a variable order method for the fast and accurate computation of the Fourier transform is presented. The increase in accuracy is achieved by applying corrections to the trapezoidal sum approximations obtained by the FFT method. It is shown that the additional computational work involved is of orderK(2m+2), wherem is a small integer andKn. Analytical expressions for the associated error is also given.     

Truncation error in interpolation and numerical differentiation

Summary A bound is obtained for the error incurred when derivatives are found in terms of differences. The method depends on the use of an auxiliary function, and it is shown that by appropriately choosing the auxiliary function one may considerably improve the estimate of the error, especially in the neighbourhood of a singularity. The result, in addition, provides an alternative form for the remainder term in interpolation formulae, and it can also be regarded as an extension of Cauchy's generalised mean-value theorem.