On bimeasurings II

We answer some questions posed in [L. Grunenfelder, M. Mastnak, On bimeasurings, J. Pure Appl. Algebra 204 (2006) 258-269] concerning the universal bimeasuring bialgebra via a construction of suitable subcoalgebras of the universal measuring coalgebra.     

Convergence of generalized conjugate partial Fourier integrals

Generalized conjugate partial Fourier integrals are used to find jumps of functions. The rate of convergence is studied and sharp results are obtained.     

On the level density of random band matrices

Translated from Matematicheskie Zametki, Vol. 50, No. 6, pp. 31–42, December, 1991.     

Early Evolution of Gas Chromatography in East Germany. Part I: Beginnings, Instrument and Column Development and Organizations

The early evolution of gas chromatography in the former German Democratic Republic (GDR) is surveyed and instrument development is outlined, describing the most important models manufactured in the GDR. The organization of the Arbeitsgemeinschaft für Gas-Chromatographie (Working Group for GC) is chronicled and its activities are discussed. Subsequent parts of this article will deal with the six symposia organized by the Arbeitsgemeinschaft between 1958 and 1968.     

High-Throughput Screening of Ten Microcystins and Nodularins, Cyanobacterial Peptide Hepatotoxins, by Reversed-Phase Liquid Chromatography-Electrospray Ionisation Mass Spectrometry

Liquid chromatography-electrospray ionisation mass spectrometry was evaluated in the high-throughput analysis of microcystins and nodularins, cyanobacterial peptide hepatotoxins. Extracts originating from cyanobacterial strains and field material were separated on a 30 mm × 4 mm I.D. Merck Purospher STAR RP-18e column using a rapid gradient of aqueous formic acid and acetonitrile, ionised by electrospray technique and analysed on a Micromass Quattro II triple-quadrupole mass spectrometer operated in the selected ion recording (SIR) mode. The total analysis time per sample was 2.8 min corresponding to 514 samples a day. The system showed good robustness during a series of 320 repetitive injections of a field sample containing three major microcystins.     

Pointwise and L2 bounds in some nonstandard problems for the heat equation

We consider some initial-boundary value problems for the linear and nonlinear heat equation where the gradient of the solution is prescribed on the boundary. Assuming that a solution exists, we obtain bounds for the solution and its gradient by maximum principle arguments or by means of differential and integral inequalities.     

Photon statistics in the stochastic limit of QED without dipole approximation

In this paper we investigate the distribution of the Heisenberg evolution of the number operator in the stochastic limit of the quantum electromagnetic field without dipole approximation. We prove that in this case the usual Poisson statistics of the free fields has to be replaced by a hypergeometric series whose coefficients we compute explicitly. The physical effects of the new statistics should manifest themselves in situation which are not yet in the relativistic regime, but in which the dipole approximation is no longer valid. The text was submitted by the authors in English.     

Cluster sets of subharmonic functions and associated measures in a cone

A study is conducted of the relationship between the asymptotic behavior of a subharmonic function of finite order in a cone and the distribution of the measure associated with it.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 247–261, Febraury, 1991.     

On the instability of parallel weakly interacting dislocations in soft-mode crystals

The instability of the rectilinear form of parallel weakly interacting dislocations, manifesting itself in their spontaneous wave-like bending, has been investigated. It is shown that softening of a crystal leads to the enhancement of this instability.