1H, 13C and 15N NMR spectral analysis of substituted 1,2,3,4‐tetrahydro‐pyrido[1,2‐a]pyrimidines

The NMR spectroscopic data of a series of thirty‐four 3‐acylpyrido[1,2‐a]pyrimidinium salts are analyzed, which were prepared as either perchlorates or chlorides. Methyl group substituted 3‐aroyltetrahydropyrido[1,2‐a]pyrimidines with the methyl substituent in positions 6, 8 and 9 as well as both in positions 6 and 8 were investigated bearing various aroyl substituents. Unequivocal assignment of all resonances was achieved via two‐dimensional ¹H,¹H‐COSY measurements, ¹H,¹³C and ¹H,¹⁵N HSQC as well as HMBC experiments, and important diagnostic CH and NH couplings in the heteroaromatic ring system are evaluated. The influence of the methyl substituents was analyzed on the proton, carbon and nitrogen shifts. A significant effect of the counter ion on some chemical shifts of the nuclei under discussion of the pyridopyrimidines is found, allowing the indirect detection of the anion, which is confirmed by direct measurement of the ³⁵Cl nucleus of the perchlorates. Copyright © 2013 John Wiley & Sons, Ltd.     

The μSR facilities at PSI

TheSR Facility Instruments presently available at PSI and the envisaged medium- and long-term developments are presented. The plans focus on further upgrades of the existing instruments and the development of new techniques using the very high fluxes becoming available at PSI, in particular the setup of a beamline with a fast kicker for muons on request (MORE) and the development of very low energy muon beams.     

Über die Primteiler-Anzahl ω(n)

It is shown by analytical means that, if one assumes the Riemann hypothesis, the asymptotic formula $$\sum\limits_{n \leqslant x} {\omega (n) = x 1n1n } x + B - x\int_l^{x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } {\frac{{\{ t\} }}{{t^2 (1n x - 1n t)}}dt + O(x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon } )} $$ holds. This improves a result ofB. Saffari, who got a weaker error term by using the Dirichlet “hyperbola method”. The above formula, in turn, implies the Riemann hypothesis.     

Energy-transport by radiative diffusion

A new derivation of the general-relativistic Fourier equation is given for radiation transport by using the principle of conservation of momentum plus some rather simple assumptions. The Fourier equation at which I arrive is not the usual one but has an additional term. For this reason it leads to a hyperbolic equation for heat conduction, thus avoiding the paradox of infinite velocity of heat propagation, which is a consequence of the usual Fourier equation, as the latter one leads to a parabolic equation for heat conduction. The new Fourier equation is compared with the one that was given by Kranys by using ad hoc assumptions.     

Estimation of lake water—groundwater interactions in meromictic mining lakes by modelling isotope signatures of lake water

Abstract

A method is presented to assess lake water–groundwater interactions by modelling isotope signatures of lake water using meteorological parameters and field data. The modelling of δ¹⁸O and δD variations offers information about the groundwater influx into a meromictic Lusatian mining lake. Therefore, a water balance model is combined with an isotope water balance model to estimate analogies between simulated and measured isotope signatures within the lake water body. The model is operated with different evaporation rates to predict δ¹⁸O and δD values in a lake that is only controlled by weather conditions with neither groundwater inflow nor outflow. Comparisons between modelled and measured isotope values show whether the lake is fed by the groundwater or not. Furthermore, our investigations show that an adaptation of the Craig and Gordon model [H. Craig, L.I. Gordon. Deuterium and oxygen-18 variations in the ocean and the marine atmosphere. In Stable Isotopes in Oceanographic Studies and Paleotemperature, Spoleto, E. Tongiorgi (Ed.), pp. 9–130, Consiglio Nazionale delle Ricerche, Laboratorio di Geologia Nucleare, Pisa (1965).] to specific conditions in temperate regions seems necessary.     

4-Dimensional black holes from Kaluza-Klein theories

In this paper we consider generalizations in 4 dimensions of the Einstein-Maxwell equations which typically arise from Kaluza-Klein theories. We specify conditions such that stationary solutions lead to non-linear-models for symmetric spaces. Using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in Einstein-Maxwell theory to this more general setting.     

Finite-size scaling in a microcanonical ensemble

The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz.     

On the gap problem for the sequence ∥mβ∥

We discuss the gap problem for the sequence m used in our previous Letter (D. H. Mayer, Lett. Math. Phys. 16, 139–143 (1988)).     

Dynamic percolation transition induced by phase separation: A Monte Carlo analysis

The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider quenching experiments, where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki spinexchange dynamics. Analyzing the distributionn _l(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly lower than the percolation concentration of the initial random state. This dynamic percolation transition is analyzed with finite-size scaling methods. While at zero temperature, where the system settles down at a frozen-in cluster distribution and further phase separation stops, the critical exponents associated with this percolation transition are consistent with the universality class of random percolation, the critical behavior of the transient time-dependent percolation occurring at nonzero temperature possibly belongs to a different, new universality class.