Associated Primes of the Example of Brenner and Monsky

Recently, Brenner and Monsky found an example of an ideal in a hypersurface ring whose tight closure does not commute with localization, thus answered the localization problem in tight closure theory in the negative. In this article, we use Monsky's calculations to analyze the set of associated primes of the Frobenius powers of this ideal and show that this set is infinite.     

A 15N labelling,FD and FAB study of ammonia loss from protonated arginine molecules

The positive ion field desorption (FD) spectrum of arginine taken at the best anode temperature only contains a peak due to [M+H]⁺ ions. At higher emitter temperatures a considerable amount of fragmentation is induced and the [M+H NH₃]⁺ ions become most abundant. Specific ¹⁵N labelling reveals that the eliminated ammonia molecule, exclusively, contains one of the terminal nitrogen atoms of the guanidyl group. This also applies to the ammonia loss from metastably decomposing [M+H]⁺ ions. The positive ion fast atom bombardment (FAB) spectrum shows more fragmentation than the FD spectrum. In contrast with the FD results, the [M+H]⁺ ions generated upon FAB with ion lifetimes <10⁻⁶ s eliminate both ammonia containing one of the terminal nitrogen atoms of the guanidyl group and ammonia containing the α-amino group in the ratio of 1.35, as found by ¹⁵N labelling. The metastably decomposing [M+H]⁺ ions, however, eliminate only the former ammonia molecule. In the negative ion FD and FAB spectra no other peak than that corresponding to the [M H]⁻ ion is observed. Some attention has been paid to the thermal degradation of arginine on the basis of a few Curie-point pyrolysis experiments.     

Observation of concentration boundary layers around growing or dissolving KH2PO4 crystals in stagnant solutions

The solute concentration profiles around KH₂PO₄ crystals growing or dissoloving in stagnant aqueous solutions were studied by the schlieren method after Toepler. By this technique the thicknesses of concentration boundary layers around the crystals, formed by free convection of solution, were measured in dependence of crystal size and super (under) saturation. In the case of dissolution, theoretical estimation of the boundary layer thickness yielded a fair agreement with the observed value. For growth, the process is dominantly limited by surface kinetics, whereas volume diffusion plays a minor role.     

Optimal dispatching in a tandem queue

Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of Lévy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can be significant.     

A feedback fluid queue with two congestion control thresholds

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold B ₁ is used to signal the beginning of congestion while the lower threshold B ₂ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold B ₁ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until B ₂ (smaller than B ₁) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.     

A minimization version of a directed subgraph homeomorphism problem

We consider a special case of the directed subgraph homeomorphism or topological minor problem, where the host graph has a specific regular structure. Given an acyclic directed pattern graph, we are looking for a host graph of minimal height which still allows for an embedding. This problem has applications in compiler design for certain coarse-grain reconfigurable architectures. In this application domain, the task is to simultaneously schedule, bind and route a so-called data-flow graph, where vertices represent operations and arcs stand for data dependencies between the operations, given an orthogonal grid structure of reconfigurable processing elements (PEs) that have restricted communication abilities. We show that the problem of simultaneously scheduling, binding and routing is NP-complete by describing a logic engine reduction from NAE-3-SAT. This result holds even when the input graph is a directed tree with maximum indegree two. We also give a |V|^3/2-approximation algorithm. J. A. Brenner’s research supported by the DFG Research Center Matheon “Mathematics for key technologies”. J. C. van der Veen’s research supported by DFG Focus Program 1148, “Reconfigurable Architectures”, Grants FE 407/8-1 and FE 407/8-2.     

Hydrogen interaction with EUVL-relevant optical materials

Mo/Si multilayer mirrors were exposed to deuterium ions with well-defined energies in order to gain insight into the effects of Extreme UV light driven plasma generation on reflective elements in commercial lithography equipment. Post-irradiation analysis by Rutherford Backscattering Spectrometry showed erosion of both Mo and Si layers for the highest energy 50 eV/D and exposure time 5.4 × 10⁴ s. Nuclear Reaction Analysis revealed detectable deuterium retention for energies ⩾25 eV/D. Surface analysis by X-ray Photoelectron Spectroscopy showed erosion of the first Si layer for energies ⩾5 eV/D. Inferences on the spatial distribution of trapped deuterium are made on the basis of available data regarding deuterium retention in the materials in question.