Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

ken

From the beginning, the world of game-playing by machine has been fortunate in attracting contributions from the leading names of computer science. Charles Babbage, Konrad Zuse, Claude Shannon, Alan Turing, John von Neumann, John McCarthy, Alan Newell, Herb Simon and Ken Thompson all come to mind, and each reader will wish to add to this list. Recently, the Journal has saluted both Claude Shannon and Herb Simon. Ken’s retirement from Lucent Technologies’ Bell Labs to the start-up Entrisphere is also a good moment for reflection.

Effect of drainage and wildfire on peat hydrophysical properties

Consecutive multiple disturbances to northern peatlands can dramatically impact peat hydrophysical properties. We examine the impact of a double disturbance (drainage and wildfire) on the hydrophysical and moisture retention properties of peat, a key regulator of peatland ecohydrological resilience, and compare this with the impact to each individual disturbance (drainage and wildfire). The compound effect of drainage and wildfire resulted in a shift of the surface datum down the peat profile, revealing denser peat. Less-dense near-surface peats that regulate water-table position and near-surface moisture content, both favourable to Sphagnum recolonization, were lost. At a drained peatland that was then subject to wildfire, peat bulk density increased by 14.1%, von Post humification class increased by two categories and water retention increased by 15.6%, compared with an adjacent burned but undrained (single disturbance) portion of the fen. We discuss the key hydrophysical metrics of peatland vulnerability and outline how they are affected by the isolated impacts of drainage and wildfire, as well as their combined effects. We demonstrate that multiple peatland disturbances have likely led to an increase in hydrological limitations to Sphagnum recovery, which may impact peatland ecohydrological resilience.

Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models

With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally-explicit vertically-implicit (HEVI) time-stepping schemes warrant further attention. In this analysis, Runge-Kutta implicit-explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non-divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next-generation high-resolution weather models to coarse-resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability-constrained shorter time-steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval. Two schemes, “Trap2(2,3,2)” and “UJ3(1,3,2)”, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, “Trap2(2,3,2)” is the least expensive.

Transmathematical basis of infinitely scalable pipeline machines

We describe infinitely scalable pipeline machines with perfect parallelism, in the sense that every instruction of an inline program is executed, on successive data, on every clock tick. Programs with shared data effectively execute in less than a clock tick. We show that pipeline machines are faster than single or multi-core, von Neumann machines for sufficiently many program runs of a sufficiently time consuming program. Our pipeline machines exploit the totality of transreal arithmetic and the known waiting time of statically compiled programs to deliver the interesting property that they need no hardware or software exception handling.

Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.

Inverting the lives of 'others': retelling the Nazi past in 'Ehe im Schatten' and 'Das Leben der Anderen'

The article compares Florian Henckel von Donnersmarck's film Das Leben der Anderen (2006) with Kurt Maetzig's early post-war film Ehe im Schatten (1947). The comparison is based on significant narrative and thematic elements which the films share: They both have a ‘theatre couple’, representatives of the ‘Bildungsbürgertum’, at the centre of the story; in both cases the couple faces a crisis caused by the first and second German dictatorship respectively and then both try to solve the crisis by relying on the classical ‘bürgerliches Erbe’, particularly the ‘bürgerliches Trauerspiel’. The extensive use of the ‘bürgerliches Erbe’ in the films activates the function this heritage had for the definition of the German nation in the nineteenth century. However, while Maetzig's film shows how the ‘heritage’ and its representatives fail in the face of National Socialism, von Donnersmarck's film claims the effectiveness of this ‘heritage’ in the fight against the East German dictatorship. Von Donnersmarck thus inverts a critical film tradition of which Ehe im Schatten is an example; furthermore, as this tradition emerged from dealing with the Third Reich, von Donnersmarck's film, it will be argued, is more interested in the redemption of the Nazi past than the East German past.