Radiocaesium pollution of fly agaric Amanita muscaria in fruiting bodies decreases with developmental stage

Amanita muscaria collected from a forested area in northern Poland in 2015 were analysed for activity concentrations of ¹³⁷Cs and ⁴⁰K. Total K concentration values were calculated from ⁴⁰K data. Mushrooms were grouped in six fruiting bodies size classes regarding to their developmental stage. The ¹³⁷Cs activity concentrations declined in A. muscaria as the fruiting bodies maturated. The contents of ⁴⁰K/K activity remained constant in caps at different developmental stage, while for stipes an increase was around twofold (⁴⁰K from 925?±?55 Bq kg^?1 dry biomass in the baby individuals and 1600?±?63–1700?±?53 Bq kg^?1 dry biomass in two oldest classes). A. muscaria is a weak accumulator of ¹³⁷Cs, while a steep drop in activity concentrations of this nuclide in the fruiting bodies as they maturate has not been reported earlier for mushrooms. Clearly, a fate of ¹³⁷Cs in A. muscaria is highly different from that of ⁴⁰K/K that is an essential element to fungi. In parallel, an observed increase in the content of ⁴⁰K/K in stipes of fruiting bodies with developmental state can be related to its ‘hardening’ and more fibrous nature with age and basic function to support the cap, but this has not been studied.     

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

Deformed preprojective algebras of generalized Dynkin type

We introduce the class of deformed preprojective algebras of generalized Dynkin graphs (), (), , , and () and prove that it coincides with the class of all basic connected finite-dimensional self-injective algebras for which the inverse Nakayama shift of every non-projective simple module is isomorphic to its third syzygy .

     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.     

Tame kernels of cubic cyclic fields

There are many results describing the structure of the tame kernels of algebraic number fields and relating them to the class numbers of appropriate fields. In the present paper we give some explicit results on tame kernels of cubic cyclic fields. Table 1 collects the results of computations of the structure of the tame kernel for all cubic fields with only one ramified prime

In particular, we investigate the structure of the 7-primary and 13-primary parts of the tame kernels. The theoretical tools we develop, based on reflection theorems and singular primary units, enable the determination of the structure even of 7-primary and 13-primary parts of the tame kernels for all fields as above. The results are given in Tables 2 and 3.

     

On linear congruence relations for Kubota-Leopoldt 2-adic L-functions

Our purpose in the paper is to find the most general linear congruence relation of the Hardy-Williams type for linear combinations of special values of Kubota-Leopoldt 2-adic L-functions L₂(k,χω^1−k) with k running over any finite subset of not necessarily consisting of consecutive integers (see Acta Arith. 47 (1986) 263; Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, 1995/1996; Publ. Math. Debrecen 56 (2000) 677 and cf. Mathematics and Its Applications, Vol. 511, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000). If k runs over finite subsets of consisting of consecutive integers see Compositio Math. 111 (1998) 289; Publ. Math. Debrecen 56 (2000) 677; Hardy and Williams, 1986; Compositio Math. 75 (1990) 271; Acta Arith. 71 (1995) 273; 52 (1989) 147; J. Number Theory 34 (1990) 362. In order to obtain the most general congruences of this type we make use of divisibility properties of the generalized Vandermonde determinants obtained in Spie? et al. (Divisibility properties of generalized Vandermonde and Cauchy determinants, Preprint 627, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 2002). This allows us to simplify our main Theorem 2 and obtain Theorem 3 where the most general form of the linear congruence relation is given.     

The electron affinity of Al13H cluster: high level ab initio study

Al₁₃H clusters have been considered candidates for cluster assembled materials. Here we have carried out benchmark calculations for the Al₁₃H cluster, both neutral and anionic, with the aim of verifying the nature of stationary points on the potential energy surface, studying dynamics of H atom and determining an adiabatic electron affinity. A range of correlated methods applied include second-order perturbation theory (MP2), spin-component-scaled MP2, coupled electron pair (CEPA) and coupled cluster singles and doubles with perturbative triple corrections (CCSD(T)). These methods are used in combination with the correlation consistent basis sets through aug-cc-pVTZ including extrapolation to the complete basis set (CBS) limit. Performance of several different flavours of density functional theory (DFT) such as generalised gradient approximation (GGA), hybrid GGA, meta-GGA and hybrid-meta-GGA is assessed with respect to the ab initio correlated reference data. The harmonic force constant analysis is systematically performed with the MP2 and DFT methods. The MP2 results show that for neutral Al₁₃H only the hollow structure is a potential energy minimum, with the bridged structure being a transition state for the H shift from the hollow site to the adjacent hollow site. The CCSD(T)/aug-cc-pVTZ (CCSD(T)/CBS) estimate of the energy barrier to this H shift is 2.6 (2.9) kcal/mol, implying that the H atom movement over the Al₁₃H cluster surface is facile. By contrast, the DFT force constant analysis results suggest additional terminal and bridged minima structures. For the anion Al₁₃H^?, exhibiting ‘stiffer’ potential energy surface compared to the neutral, the existence of the hollow and terminal isomers is consistent with the earlier photoelectron spectroscopy assignment. The adiabatic electron affinity of Al₁₃H is determined to be 2.00 and 1.95 eV (the latter including the ΔZPE correction) based on the CCSD(T) energies extrapolated to the CBS limit, whereas the respective CCSD(T)/CBS thermodynamic EA values are 2.79 and 2.80 eV.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chieX Chandler Davis.     

Hydration-dependent structural deformation of guanine in the electronic singlet excited state

Theoretical study was performed to investigate how the degree of hydration affects the structures and properties of the canonical form (keto-N9H) of guanine in the ground and lowest singlet pipi* excited state. This work is the continuation of our earlier work where we have studied the hydration of guanine in the first solvation shell with one, three, five, and six water molecules. In the present investigation, we have considered 7-13 water molecules in hydrating guanine. Ground-state geometries were optimized at the Hartree-Fock level, whereas the configuration interaction-singles (CIS) method was used for the excited-state geometry optimization. The 6-311G(d,p) basis set was used in all calculations. The harmonic vibrational frequency analysis was used to determine the nature of the optimized ground- and excited-state potential energy surfaces; all geometries were found to be minima at the respective potential surfaces. It was found that the degree of hydration has a significant influence on the excited-state structural nonplanarity of guanine. It is expected that excited-state dynamics of guanine will depend on the degree of hydration. Ground- and excited-state geometries of selected hydrated species were also optimized in the bulk water solution using the polarizable continuum model (PCM). It was found that bulk water solution generally does not have significant influence on the structure of the hydrated species. Effects of hydration on different stretching vibrations in the ground and excited states are also discussed.