Characterization of asymptotic distribution functions of ratio block sequences

In this paper we give necessary and sufficient conditions for the block sequence of the set X = {x ₁ < x ₂ < … < x _n < …} ⊂ ℕ to have an asymptotic distribution function in the form x ^λ.     

Light Element Analysis of Individual Microparticles Using Thin-Window EPMA

 The determination of the concentration of light elements, such as carbon, nitrogen and oxygen, in e.g. atmospheric aerosol particles is important to study the chemical behaviour of atmospheric pollution. The knowledge of low-Z element concentrations gives us information on the speciation of nutrients (species having nutritional value for plants) and toxic heavy metals in the particles. The capability of the conventional energy-dispersive EPMA is strongly limited for the analysis of low-Z elements, mainly because the Be window in the EDX detector hinders the detection of characteristic X-rays of light elements such as C, N, O and Na. WDS is suitable for analysis of light elements, but the measurement of beam sensitive microparticles requires the minimisation of the beam current and the measurement time. A semi-quantitative analytical method based on EPMA using an ultra-thin window EDX detector was developed. It was found that the matrix and geometric effects that are important for low-energy X-rays can be reliably evaluated by Monte Carlo calculations. Therefore, the quantification part of the method contains reverse Monte Carlo calculation done by iterative simulations. The method was standardised and tested by measurements on single particles with known chemical compositions. Beam-sensitive particles such as ammonium-sulphate and ammonium-nitrate were analysed using a liquid nitrogen cooled sample stage. The shape and size of the particles, which are important for the simulations, were determined using a high-magnification secondary electron image. Individual marine aerosol particles collected over the North Sea by a nine-stage Berner cascade impactor were analysed using this new method. Preliminary results on five samples and 4500 particles show that the method can be used to study the modification of sea-salt particles in the troposphere.     

A wavelet-based adaptive method for determining eigenstates of electronic systems

The possibilities for reducing the necessary computation power in wavelet-based electronic structure calculations are studied. The expansion of the expectation values of energy operators, the integrals of basis functions are mostly system-independent, consequently it is not necessary to compute them in each calculations. Fixed building blocks, such as a parameterized expansion of the nuclear and electron–electron cusp can reduce the amount of necessary calculation. An algorithm for local expansion refinement is also given. It is possible to determine the significant expansion coefficients of a high resolution level without solving the Schrödinger equation using only lower resolution results.     

Conductance noise spectrum of mesoscopic systems

We investigate the shape as well as the size- and temperature-dependence of the conductance noise spectrum of a small system containing electrons and both fixed and mobile scatterers. If the number of mobile scatterers within a phase-coherent region is sufficiently large, the temporal variation of the conductance can be viewed as a random walk process limited by the universal conductance fluctuations, resulting in a practically Lorentzian power spectrum. We discuss the conditions under which the noise spectrum of a system consisting of many phase-coherent regions is either Lorentzian or 1/f-like. The temperature-dependence of the power spectrum is determined by the hopping mechanism and the variation of the phase breaking length. As a function of temperature the spectrum satisfies power law scaling relations with exponents depending on the dimension and the temperature range; the spectral intensity can both increase and decrease with decreasing temperature.     

Effective Nullstellensatz for arbitrary ideals

Let f _i be polynomials in n variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials g _i such that ∑g _i f _i =1. The effective versions of this result bound the degrees of the g _i in terms of the degrees of the f _j . The aim of this paper is to generalize this to the case when the f _i are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed. Received August 24, 1998 / final version received June 21, 1999     

On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions

The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.     

Radiochemical characterization of spring waters in Balaton Upland, Hungary, estimation of radiation dose to members of public

Hungary is rich in spring waters. A survey studying the naturally occurring alpha emitter radionuclides in 30 frequently visited and regularly consumed spring waters was conducted out in the Balaton Upland region of Hungary.²²⁶Ra, ²²⁴Ra, ²³⁴U, ²³⁸U and ²¹⁰Po activity concentrations were determined by using alpha spectrometry after separation from matrix elements. Average concentration (mBq L^{− 1}) of ²²⁶Ra, ²²⁴Ra, ²³⁴U, ²³⁸U and ²¹⁰Po in the spring waters is varied from 2.1 to 601, from < 1.1 to 65.4, from 3.9 to 741.9, from < 0.44 to 274.3 and from 2 to 15.2 respectively. In most cases radioactive disequilibrium was observed between uranium and radium isotopes. The doses for the analyzed samples of spring water are in the range 3.59–166.73 μSv y^{− 1} with an average 18.2 μSv y^{− 1} .This is well below the 100 μSv y^{− 1} reference level of the committed effective dose recommended by WHO. Only one water sample had a dose higher than 100 μSv y^{− 1}, mainly due to the contribution from radium (²²⁶Ra, ²²⁴Ra) and ²¹⁰Po isotopes. This study provides important information for consumers and authorities about their internal radiological exposure risk from spring water intake.