Tail asymptotics for M/G/1 type queueing processes with subexponential increments

Bivariate regenerative Markov modulated queueing processes {I _n ,L _n } are described. {I _n } is the phase process, and {L _n } is the level process. Increments in the level process have subexponential distributions. A general boundary behavior at the level 0 is allowed. The asymptotic tail of the cycle maximum, , during a regenerative cycle, , and the asymptotic tail of the stationary random variable L _∞, respectively, of the level process are given and shown to be subexponential with L _∞ having the heavier tail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dynamics of money

We present a dynamical many-body theory of money in which the value of money is a time dependent "strategic variable" that is chosen by the individual agents. The value of money in equilibrium is not fixed by the equations, and thus represents a continuous symmetry. The dynamics breaks this continuous symmetry by fixating the value of money at a level which depends on initial conditions. The fluctuations around the equilibrium, for instance in the presence of noise, are governed by the "Goldstone modes" associated with the broken symmetry. The idea is illustrated by a simple network model of monopolistic vendors and buyers.     

Small degree out‐branchings

Using a suitable orientation, we give a short proof of a strengthening of a result of Czumaj and Strothmann 4 : Every 2‐edge‐connected graph G contains a spanning tree T with the property that for every vertex v. As an analogue of this result in the directed case, we prove that every 2‐arc‐strong digraph D has an out‐branching B such that . A corollary of this is that every k‐arc‐strong digraph D has an out‐branching B such that , where . We conjecture that in this case would be the right (and best possible) answer. If true, this would again imply a strengthening of a result from 4 concerning spanning trees with small degrees in k‐connected graphs when k ≥ 2. We prove that for acyclic digraphs the existence of an out‐branching satisfying prescribed bounds on the out‐degrees of each vertex can be checked in polynomial time. A corollary of this is that the existence of arc‐disjoint branchings , , where the first is an out‐branching rooted at s and the second an in‐branching rooted at t, can be checked in polynomial time for the class of acyclic digraphs © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 297–307, 2003     

A comparison of psychophysical procedures for level-discrimination thresholds

Five different psychophysical procedures were used to measure level-discrimination (also called intensity discrimination) thresholds for 1-kHz tones at two levels (30 and 90 dB SPL) and two durations (10 and 500 ms). The procedures were the classic transformed up-down staircase method with a two-alternative forced-choice (2AFC) paradigm (UPD), 15- and 50-trial implementations of the method of maximum likelihood (MML) with a cued yes-no paradigm, and 18-trial implementations of ZEST using both cued yes-no and 2AFC paradigms. Results obtained from nine normal listeners show that estimates of level-discrimination thresholds for the four conditions are similar across all five procedures when different points of convergence are accounted for. The variance of threshold estimates within listener and condition was smallest for UPD, largest for the MML with 15 trials, and statistically indistinguishable among the others. The sweat factors ranged from 5.5 for MML with 50 trials to about 1.4 for UPD and ZEST. Simulations show that ideal performance of procedures may be far from real-life experience and that these deviations are likely to depend on complex interactions between listener behavior and parameter choices used for implementing the procedures. Therefore, empirical verification is important for judging the effectiveness of psychophysical procedures.     

Improved estimation of the ranking probabilities in partial orders using random linear extensions by approximation of the mutual ranking probability

The application of partial order theory and Hasse diagram technique in environmental science is getting increasing attention. One of the latest developments in the field of Hasse diagram technique is the use of random linear extensions to estimate ranking probabilities. In the original algorithm for estimating the ranking probability it is assumed that the order between two incomparable pair of objects can be chosen randomly. However, if the total set of linear extensions is considered there is a specific probability that one object will be larger than another, which can be far from 50%. In this study it is investigated if an approximation of the mutual ranking probability can improve the algorithm. Applying an approximation of the mutual ranking probability the estimation of the ranking probabilities are significantly improved. Using a test set of 39 partial orders with randomly chosen values the relative mean root square difference (MRSD) decrease in average from 7.9% to 2.2% and a maximum relative improvement of 90% can be found. In the most successful case the relative MRSD goes as low as 0.77%.     

Single-mode operation of a laser-diode array with frequency-selective phase-conjugate feedback

A new technique for single-mode operation of laser-diode arrays is presented. A gain-guided GaAlAs laser diode array is coupled to an external frequency-selective phase-conjugate feedback system that contains a photorefractive barium titanate crystal, a Fabry-Perot etalon, and a spatial filter. The etalon is the key component, and it forces the array, which has low spatial and spectral coherence when it runs freely, to oscillate in a single spatial and a single longitudinal mode. At a drive current of two times the threshold current, the far-field pattern is reduced to only 1.4 times the diffraction limit, the spectral bandwidth is less than 0.02 nm, and the coherence length is increased by a factor of 70. The technique has general validity and can be applied to various other multimode laser systems.     

High-reflectivity fiber-optic bandpass filter designed by use of the iterative solution to the Gel'fand-Levitan-Marchenko equations

A fiber Bragg grating bandpass filter has been investigated. The profile of the 3.1-cm-long grating was synthesized for high reflectivity and low dispersion by use of the iterative solution to the Gel'fand-Levitan-Marchenko equations. A grating designed according to this synthesis was written into a boron-codoped germanosilica fiber. The measured spectral response was in good agreement with simulations. The achieved in-band reflection was 97%, and the passband ripple was only 0.06 dB.     

Methods for chemical analysis of contaminated soil samples--tests of their reproducibility between Nordic laboratories

In an effort to develop common analytical methods for contaminated soil samples the Environmental Authorities of the Nordic countries have, together with Nordtest, published the report Nordic Guidelines for Chemical Analysis of Contaminated Soil Samples. The aim of these guidelines has been to describe analytical methods which could be accepted in all the Nordic countries and in that way contribute to reducing the variation in the analytical results between laboratories. The methods covered, reflects environmental concerns and priorities in the Nordic countries for now, i.e. heavy metals, chlorophenols, creosote, volatile organic compounds, PCB, THC and PAH. The repeatability and reproducibility of the guideline methods were determined in a Nordic inter-laboratory test in 1996, and the results showed some variations. The analytical methods and the results from the inter-laboratory tests are given for heavy metals, chlorophenols, creosote, volatile organic compounds and PCB.     

Multistep determination of enzyme activity by flow injection and sequential injection analysis. Assay of amyloglucosidase

A multi-point assay for determination of the activity of amyloglucosidase (AMG) by FIA and SIA is described. The assay is based on two consecutive reactions that are mutually incompatible. Both the FIA and SIA procedures allow these two reactions to be completely separated, whereby each of the processes can be individually optimized with respect to operational parameters. Special emphasis is placed on comparing the performance and applicability of the two procedures for this type of assay.     

Kekulé structure counts: General formulations for primitive coronoid hydrocarbons

Summary The Kekulé structure counts (K) for primitive coronoids are treated. TheK formula which involves the trace of a matrix product is recalled and supplemented with new findings. In this way a kind of symmetry in the mathematical formulations is restored. Another general formulation for theK number is provided in terms of polynomials which, for a somewhat mysterious reason, are identified as the matching polynomials of cycles.

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Zählung von Kekulé-Strukturen

Zusammenfassung Es werden Kekulé-Strukturzählungen (K) für einfache Coronoide behandelt. Die Formel fürK wird durch neugefundene Eigenschaften ergänzt. So wird eine Art von Symmetrie in den mathematischen Formulierungen erreicht. Eine andere generelle Formulierung derK-Zahlen wird in Form von Polynomen bereitgestellt, welche aus uneinsichtigen Gründen als die passenden Polynome von Cyclen identifiziert wurden.