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.     

Experimental confirmation by galvanomagnetic methods of a complex transport model in In0.53Ga0.47As layers deposited by MBE on SI-InP

At low temperatures In_0.53Ga_0.47As samples show an increase of carrier concentration, which can be explained in terms of a two carriers transport model. This type of problem exists since the beginning of the semiconductor era, dating back to monocrystalline germanium.We propose that in all the investigated layers, there are X atoms or charged dislocations in the region of the first monolayers, which are built in during epitaxial growth. The layers were intentionally undoped. They form an impurity band in which low mobility carriers dominate over the localised electron scattering due to the s-d exchange interaction. These carriers do not freeze out at liquid helium temperature and give rise to two transport media for electrons; a conduction band at higher temperatures and an impurity band at lower temperatures. The electron which fall down onto the previously ionised X atoms, then move by thermally activated hopping. We show that the two carriers model for In_0.53Ga_0.47As epitaxial layers are confirmed by the carrier concentration-temperature, carrier concentration-magnetic field, resistivity-magnetic field behaviour, and also by YKA theory also. The differences between the two transport models are so distinctive that observed phenomena may exist. This paper presents experimental results, which constitute comprehensive evidence for the complicated structure of the semiconductor epitaxial layers on the sample of n-type In_0.53Ga_0.47As/InP layer with n=2.2×10¹⁵/cm³.     

Lower-rim versus upper-rim functionalization in di-ionizable calix[4]arene-crown-5 isomers. Synthesis and divalent metal ion extraction

Two series of di-ionizable calix[4]arene-crown-5 isomers in the cone conformation are synthesized to probe the effect of the pendant acidic group location on their metal ion extraction properties. In one series, the ionizable groups are attached to the lower rim of the calix[4]arene scaffold, which orients them near the crown ether cavity. In the second series, the ionizable groups are connected to the upper rim positioning them away from the crown ether ring, but close to the hydrophobic pocket of the calix[4]arene unit. The metal ion extraction behaviors of the two series of ligands are compared in extractions of alkaline earth metal cations, Hg²⁺, and Pb²⁺.     

K-subadditive and K-superadditive set-valued functions bounded on “large” sets

Aequationes mathematicae - We prove that every K–subadditive set–valued map weakly K–upper bounded on a “large” set (e.g. not null–finite, not...