Unsolvable Problems About Small Cancellation and Word Hyperbolic Groups

We apply a construction of Rips to show that a number of algorithmicproblems concerning certain small cancellation groups and, inparticular, word hyperbolic groups, are recursively unsolvable.Given any integer k > 2, there is no algorithm to determinewhether or not any small cancellation group can be generatedby either two elements or more than k elements. There is a smallcancellation group E such that there is no algorithm to determinewhether or not any finitely generated subgroup of E is all ofE, or is finitely presented, or has a finitely generated secondintegral homology group.     

Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions: II. The Heterogeneous Case

We consider the problem of discriminating between two independent multivariate normal populations, N_p(μ₁, Σ₁) and N_p(μ₂, Σ₂), having distinct mean vectors μ₁ and μ₂ and distinct covariance matrices Σ₁ and Σ₂. The parameters μ₁, μ₂, Σ₁, and Σ₂ are unknown and are estimated by means of independent random training samples from each population. We derive a stochastic representation for the exact distribution of the “plug-in” quadratic discriminant function for classifying a new observation between the two populations. The stochastic representation involves only the classical standard normal, chi-square, and F distributions and is easily implemented for simulation purposes. Using Monte Carlo simulation of the stochastic representation we provide applications to the estimation of misclassification probabilities for the well-known iris data studied by Fisher (Ann. Eugen.7 (1936), 179–188); a data set on corporate financial ratios provided by Johnson and Wichern (Applied Multivariate Statistical Analysis, 4th ed., Prentice–Hall, Englewood Cliffs, NJ, 1998); and a data set analyzed by Reaven and Miller (Diabetologia16 (1979), 17–24) in a classification of diabetic status.     

The structure of singly-periodic minimal surfaces

The research described in this paper was supported by research grant DE-FG02-86ER250125 of the Applied Mathematical Science subprogram of Office of Energy Research, U.S. Department of Energy, and National Science Foundation grants DMS-8611574 and DMS-8802858     

The thymine radicals and their respective anions: molecular structures and electron affinities

The adiabatic electron affinities (AEA), vertical electron affinities (VEA) and vertical detachment energies (VDE) are predicted for six different radicals derived from thymine by the removal of one hydrogen atom. Geometry optimizations were carried out utilizing the DFT functionals B3LYP, BLYP and BP86 with double-c quality basis sets plus polarization and diffuse functions (DZP++). These methods have been carefully calibrated for the prediction of electron affinities [RIENSTRA-KIRACOFE, J. C., TSCHUMPER, G. S., SCHAEFER, H. F., NANDI, S., and ELLISON, G. B., 2002, Chem. Rev., 102, 231]. All optimized structures were confirmed to be minima via vibrational frequency analyses. Both the neutrals and the anion radicals were observed to possess C_s, symmetry, conserving the parent molecule's qualitative conformation. The electron affinities ranged between 1.04 and 3.74eV for the different radicals, contrasting to the small electron affinities associated with the closed-shell thymine species. The radicals with a hydrogen atom removed from one of the nitrogens present the largest electron affinities of all six radicals investigated (3.22eV for NI and 3.74eV for N3).     

Comparison of adjoint‐based and feature‐based grid adaptation for functional outputs

Adjoint‐based and feature‐based grid adaptive strategies are compared for their robustness and effectiveness in improving the accuracy of functional outputs such as lift and drag coefficients. The output‐based adjoint approach strives to improve the adjoint error estimates that relate the local residual errors to the global error in an output function via adjoint variables as weight functions. A conservative adaptive indicator that takes into account the residual errors in both the primal (flow) and dual (adjoint) solutions is implemented for the adjoint approach. The physics‐based feature approach strives to identify and resolve significant features of the flow to improve functional accuracy. Adaptive indicators that represent expansions and compressions in the flow direction and gradients normal to the flow direction are implemented for the feature approach. The adaptive approaches are compared for functional outputs of three‐dimensional arbitrary Mach number flow simulations on mixed‐element unstructured meshes. Grid adaptation is performed with h‐refinement and results are presented for inviscid, laminar and turbulent flows. Copyright © 2006 John Wiley & Sons, Ltd.     

Radionuclide detection by ion-chromatography and on-line ICP/MS and beta detection: Fission product rare earth element measurements

Separation and analysis of²³⁵U fission produced rare earth elements (REE) is described. Rare earth elements were separated using a high presure ion chromatographic separation where by each rare earth is isolated and individually detected. Detection is performed by inductively coupled plasma mass spectrometry (ICP/MS) and solid scintillation beta counting. The resulting detection methods allow complete evaluation of all stable (non-radioactive) and many radioactive REE fission products. The two detection methods (ICP/MS and Beta) illustrate how mass selective and radiometric data can be used to provide complimentary information regarding the isotopic characterization of radioactive samples.Pacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.     

The effect of pulsed electric fields on biological cells:experiments and applications

The effect of pulsed electric fields with amplitudes in the range of 100 V/cm-100 kV/cm on bacteria and aquatic nuisance species has been explored. The pulse duration was so short that heating of the biological matter could be neglected. The electrical energy required for lysing of bacteria, or stunning of aquatic species, decreases when the pulse duration is reduced. For lysing of Eschericia coli, this tendency has been proven to hold for pulsewidths as short as 60 ns. For macroorganisms, however, it was found that for pulsewidths of less than 5 μs, the tendency is reversed: the energy required to affect the macroorganisms increases again. This minimum in energy, or maximum in efficiency, respectively, can be understood by taking the time required for electrical charging of the cell membrane into account. Applications of the pulsed electric field technique (PEFT) are in biofouling prevention, debacterialization of liquids, and in the field of medicine. A series of field tests on biofouling prevention in a cooling system with untreated water as coolant has demonstrated the economic feasibility of the electro-technology