Algebraic implications of composability of physical systems

From classical and quantum mechanics we abstract the concept of a two-product algebra. One of its products is left unspecified; the other is a Lie product and a derivation with respect to the first. From composition of physical systems we abstract the concept of composition classes of such two-product algebras, each class being a semigroup with a unit. We show that the requirement of mutual consistency of the algebraic and the semigroup structures completely determines both the composition classes and the two-product algebras they consist of. The solutions are labelled by a single parameter which in the physical case is proportional to the square of the quantum of action.     

Die Anlagerung von radioaktiven Atomen und Ionen an Aerosolteilchen

The attachment of radioactive atoms and ions to spherical aerosol particles has been studied theoretically. For uncharged atoms the deposition is considered to be solely governed by thermal diffusion. With calculations based on the “limiting-sphere”-method ofArendt-Kallman it is found, that the attached activity is proportional toΦ ² for aerosol particle diametersΦ smaller than 0.1 μm, and proportional toΦ forΦ greater than 1 μm. For charged ions the diffusion process is modified by the influence of electrostatic forces between the diffusing ions and the aerosol particles. In the frequently occurring case of a symmetrically bipolar charged aerosol this influence can be expressed by a functionG _p(Φ), which depends on the diameterΦ and the effective numberp of elementary charges on the aerosol particle. For an aerosol particle diameterΦ greater than 0.1 μm the attached activity is proportional toΦ ^1.1, and forΦ smaller than 0.01 μm it is proportional toΦ ^1.55. The effects of neglecting various terms in the calculation are considered. The distribution of natural radioactivity on atmospheric aerosols has been calculated for various particle size distributions according toJunge. The calculation shows that about 90% of the total natural activity should be attached to particles smaller thanΦ=0.5 μm, and about 35% to particles smaller thanΦ=0.1 μm. The time T_1/2, in which the concentration of the radioactive particles decreases to half the initial value, depends on the concentration of the aerosol particles and on their size distribution. For 10⁴ aerosol particles per cm³ and the size distributions mentioned,T _1/2 varies between 15 and 30 seconds for radioactive ions. For radioactive atomsT _1/2 is greater than it is for ions in the range of aerosol particle diameters belowΦ=0.25 μm, and smaller ifΦ greater than 0.25 μm.     

Analytisches Verfahren zur K/Ca-Altersbestimmung geologischer Proben

Zusammenfassung Es wird ein analytisches Verfahren zur K/Ca-Altersbestimmung geologischer Proben beschrieben. Die zur Berechnung des Alters notwendigen Gleichungen werden abgeleitet und zwei alternative, analytische Verfahren der K/Ca-Methode hinsichtlich ihrer Genauigkeit diskutiert. Wichtigste Voraussetzung für die Anwendbarkeit des Verfahrens sind genaue Calcium-Isotopenverhältnismessungen, wobei das ⁴⁰Ca/⁴²Ca-Verhältnis für die Bestimmung des relativen radiogenen ⁴⁰Ca-Anteils herangezogen wird. Das ⁴²Ca/⁴⁴Ca-Verhältnis wird als interner Standard zur Korrektur verwendet. Die Kalium- und Calciumbestimmungen in den Mineralien werden durch Flam-men-Atomemissionsspektrometrie mit einem internen Lithiumstandard bzw. durch massenspektrometrische Isotopenverdünnungsanalyse durchgeführt. Die Problematik der Kontamination bei der Aufarbeitung der Proben wird diskutiert. Die Ergebnisse der K/Ca-Datierung eines Langbeinits und eines Mikroklins stimmen gut mit denjenigen anderer Datierungsmethoden an den gleichen Proben überein. Die Reproduzierbarkeit des analytischen Verfahrens der K/Ca-Datierung wird an einigen Feldspäten gezeigt, wobei relative Standardabweichungen zwischen 1,8 und 7,6 % erreicht werden.Herr Dr. H. Klöppel war im Rahmen seiner Promotionsarbeit an den Untersuchungen über die Calciumisotopenfraktionierung am Ionenaustauscher beteiligt. Herrn Prof. A. Kröner, Universität Mainz, Herrn Prof. H. J. Lippolt, Universität Heidelberg sowie Herrn Dr. J. G. Stagman, Salisbury/Rhodesien, gilt unser Dank für die Überlassung von Mineralproben. Der Deutschen Forschungsgemeinschaft und dem Fonds der Chemischen Industrie danken wir für die finanzielle Unterstützung.     

On some generalizations of theorems by Landau and Pólya

If F(s), the Mellin transform ?(x) (real valued), satisfies certain regularity conditions and if its behaviour on the abscissa of convergence is known, then theorems of Landau and Pólya give information concerning sign changes of ?(x). In the present paper, corresponding conclusions are obtained when F(s) does not satisfy the regularity conditions of the theorems of Landau Pólya.     

Eccentricity and elliptic flow in proton-proton collisions from parton evolution

It has been argued that high-multiplicity proton-proton collisions at the LHC may exhibit collective phenomena usually studied in the context of heavy-ion collisions, such as elliptic flow. We study this issue using DIPSY—a Monte Carlo event generator based on the QCD dipole model. We calculate the eccentricity of the transverse area defined by the spatial distribution of produced gluons. The resulting elliptic flow is estimated to be about 6%, comparable to the value in nucleus-nucleus collisions at RHIC and the LHC. Experimentally, elliptic flow is inferred from the azimuthal correlation between hadrons, which receives contributions from collective flow, and from various other effects referred to as “nonflow”. We discuss how to identify in experiments the signal of flow in the presence of large nonflow effects.     

Measurement uncertainty evaluation and in-house method validation of the herbicide iodosulfuron-methyl-sodium in water samples by using HPLC analysis

A method for separation and quantitative determination of the iodosulfuron-methyl-sodium in water samples by high-performance liquid chromatography (HPLC) was developed and in-house validated in order to demonstrate its performance for monitoring of heterogeneous photocatalytic elimination of the herbicide iodosulfuron-methyl-sodium from water. Surface and ground water samples were used to demonstrate its selectivity, detection and quantification limits, linearity, trueness and precision. In addition, stability of iodosulfuron-methyl-sodium was studied in function of temperature and time. Method accuracy was quantified through measurement uncertainty estimate based on method validation data. The paper gives practical and easy to follow guidance on how uncertainty estimates can be obtained from method validation experiments. It shows that, if properly planned and executed, key precision and trueness studies undertaken for validation purposes can also provide much of the data needed to produce an estimate of measurement uncertainty. Our analytical protocol allowed us to quantify iodosulfuron-methyl-sodium in ground water and surface water in concentration level between 2.50–50.0 μmol L⁻¹ with satisfactory recoveries (99–104%) and repeatability lower or equal than 0.3% for all the matrices. We also estimated within-laboratory reproducibility over 3-month period, which was 0.7%. We proved that the method was selective for determination of iodosulfuron-methyl-sodium in the relevant matrices. Measurement uncertainty of results was evaluated to be 4.0% with 95% confidence level. After validation and measurement uncertainty evaluation steps, results obtained showed that the method can be applied to efficiently monitor heterogenous photocatalytic degradation of the herbicide iodosulfuron-methyl-sodium.     

Dinitrogen silylation and cleavage with a hafnocene complex

Silylation of a hafnocene complex containing a strongly activated dinitrogen ligand, [(η(5)-C(5)H(2)-1,2,4-Me(3))(2)Hf](2)(μ(2),η(2),η(2)-N(2)), by addition of CySiH(3) resulted in N-Si and Hf-H bond formation and a compound poised for subsequent N(2) cleavage. Warming the silane addition product to 75 °C triggered N-N scission, for which the requisite electrons were provided by silyl migration. Dinitrogen cleavage coupled to N-C bond formation was also accomplished by carbonylation of the silylated product, yielding an unprecedented μ-formamidide ([NC(H)O](2-)) ligand. Subsequent treatment with HCl yielded free formamide, demonstrating that an important organic molecule can be synthesized from N(2), CO, an organosilane, and protons.     

Electrocatalytic detection of polysaccharides at picomolar concentrations

Electroinactive polysaccharides (PS) modified by osmium(VI) complexes with nitrogenous ligands produce redox couples at carbon and mercury electrodes. We show that PS adducts with Os(VI) 2,2'-bipyridine produce at ~-1.2 V (against Ag/AgCl/3 M KCl electrode) an additional peak at mercury and solid amalgam electrodes. This peak is due to the catalytic hydrogen evolution, allowing detection of PS (such as dextran and mannan) at picomolar concentrations.