On natural homomorphisms of Witt rings

We prove that the kernel of the ring homomorphism between the Witt ring of any order of a global field and the Witt ring of the field is a nilideal.

     

Adsorptive Stripping Determination of Scandium(III) with Mordant Blue 9 on Silver Amalgam Film Electrode

A new adsorptive stripping voltammetric method for the determination of trace scandium(III) based on the adsorption of scandium(III)‐mordant blue 9 complex on the cyclic renewable mercury film silver based electrode (Hg(Ag)FE) is presented. The effects of various factors such as: preconcentration potential and time, pulse height, step potential and supporting electrolyte composition are optimized. The calibration graph is linear from 2 nM (0.09 μg L^?1) to 90 nM (4 μg L^?1) for a preconcentration time of 45 s, with correlation coefficient of 0.9995. For a Hg(Ag)FE with a surface area of 7.9 mm² the detection limit for a preconcentration time of 90 s is as low as 5 ng L^?1. The repeatability of the method at a concentration level of the analyte as low as 0.2 μg L^?1, expressed as RSD is 1.9 % (n=5). The proposed method was successfully applied and validated by studying the certified reference material (CRM 320 – river sediment) and natural samples with simultaneous recovery of Sc(III) from spiked water and sediment samples.     

Natural radioactivity in groundwater--a review

The issue of natural radioactivity in groundwater is reviewed, with emphasis on those radioisotopes which contribute in a significant way to the overall effective dose received by members of the public due to the intake of drinking water originating from groundwater systems. The term 'natural radioactivity' is used in this context to cover all radioactivity present in the environment, including man-made (anthropogenic) radioactivity. Comprehensive discussion of radiological aspects of the presence of natural radionuclides in groundwater, including an overview of current regulations dealing with radioactivity in drinking water, is provided. The presented data indicate that thorough assessments of the committed doses resulting from the presence of natural radioactivity in groundwater are needed, particularly when such water is envisaged for regular intake by infants. They should be based on a precise determination of radioactivity concentration levels of the whole suite of radionuclides, including characterisation of their temporal variability. Equally important is a realistic assessment of water intake values for specific age groups. Only such an evaluation may provide the basis for possible remedial actions.     

Omega theorems related to the general Euler totient function

We prove an omega estimate related to the general Euler totient function associated to a polynomial Euler product satisfying some natural analytic properties. For convenience, we work with a set of L-functions similar to the Selberg class, but in principle our results can be proved in a still more general setup. In a recent paper the authors treated a special case of Dirichlet L-functions with real characters. Greater generality of the present paper invites new technical difficulties. Effectiveness of the main theorem is illustrated by corollaries concerning Euler totient functions associated to the shifted Riemann zeta function, shifted Dirichlet L-functions and shifted L-functions of modular forms. Results are either of the same quality as the best known estimates or are entirely new.     

Relations among Henstock,McShane and Pettis integrals for multifunctions with compact convex values

Fremlin (Ill J Math 38:471–479, 1994) proved that a Banach space valued function is McShane integrable if and only if it is Henstock and Pettis integrable. In this paper we prove that the result remains valid also in case of multifunctions with compact convex values being subsets of an arbitrary Banach space (see Theorem 3.4). Di Piazza and Musia? (Monatsh Math 148:119–126, 2006) proved that if $X$ is a separable Banach space, then each Henstock integrable multifunction which takes as its values convex compact subsets of $X$ is a sum of a McShane integrable multifunction and a Henstock integrable function. Here we show that such a decomposition is true also in case of an arbitrary Banach space (see Theorem 3.3). We prove also that Henstock and McShane integrable multifunctions possess Henstock and McShane (respectively) integrable selections (see Theorem 3.1).     

Traveling wave solutions of a model of skin pattern formation in a singular case

We study traveling wave solutions to a system of four non‐linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the assumption that the strength of attachment of the epidermis to the basal lamina is sufficiently large, we prove the existence and uniqueness (up to a translation) of traveling wave solutions connecting two stationary states of the system with the dermis and epidermis cell densities being positive. We discuss the problem of the minimal wave speed. Copyright © 2010 John Wiley & Sons, Ltd.     

Tame Equivalence and Wild Sets

For semigroups with divisor theory we introduce an equivalence relation that preserves the p-dimensions of divisor class groups. While the approach has been motivated by the results on Hilbert-symbol equivalence in quadratic form theory over algebraic number fields, it is the purpose of the paper to generalize the setup to semigroups with divisor theory and to simplify the proofs by avoiding any ring- or number-theoretical arguments.     

Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

A family of optimization problems in a Hilbert space depending on a vector parameter is considered. It is assumed that the problems have locally isolated local solutions. Both these solutions and the associated Lagrange multipliers are assumed to be locally Lipschitz continuous functions of the parameter. Moreover, the assumption of the type of strong second-order sufficient condition is satisfied.It is shown that the solutions are directionally differentiable functions of the parameter and the directional derivative is characterized. A second-order expansion of the optimal-value function is obtained. The abstract results are applied to state and control constrained optimal control problems for systems described by nonlinear ordinary differential equations with the control appearing linearly.