On the eigenproblem for displacement integral equations

Summary This paper is concerned with the eigenproblem for displacement integral equations which have kernels that are finite cosine transforms. Previous work is extended to a broader class of kernels and the eigenfunctions are treated for the first time.This work was supported by the United States Atomic Energy Commission.     

Über ein Problem der Fließbandfertigung bei stochastischer Nachfrage

Zusammenfassung Bei der Fließbandfertigung mit stochastischer Nachfrage interessiert man sich für die Anpassung der Produktion an die Marktgegebenheiten. Es wird die Produktion eines Gutes betrachtet. Der Unternehmung stehen mehrere gleichwertige Fertigungsstraßen zur Verfügung. Es wird angenommen, daß alle in Betrieb befindlichen Fertigungsstraßen den gleichen und unveränderlichen Output pro Zeiteinheit haben. Gesucht ist ein optimales Verhalten, das die diskontierte Summe der zu erwartenden Kosten minimiert. Es ist naheliegend, Verfahren der dynamischen Programmierung zu verwenden. Für das Modell wird der Fall zyklischer Kontrolle betrachtet. Die Verteilung der Nachfrage während der Kontrollperioden sei bekannt, konstant, und es gelte stochastische Unabhängigkeit für verschiedene Perioden. Überschreitet die Nachfrage den Lagerbestand, dann erfolgen für den fehlenden Output Vormerkungen. Die Belieferung findet später statt.

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Summary In assembly line production with stochastic demand one is interested in the adaption of the output to the market situation. The production of one product is considered. The company has several assembly lines of the same type. It is assumed that the assembly lines in action have the same, and a constant output rate. An optimal policy, minimizing the expected value of the total discounted costs, has to be found. It is concievable that the method of dynamic programming should be used. In the model the case of cyclic control is considered. The distribution of demand during each control period is given, constant, and there is stochastic independence for different periods. If the demand exceeds the stock the deficient output is noted and delivery takes place later.

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Vorgel. v.:W. Wittmann, Heidelberg.     

A duality theorem for continuous-time linear programming problems

Summary In dealing with dynamic economic policy models one encounters optimization problems whose objective function is an integral of a linear function of a finite number of continuous variables and whose constraints are linear integral inequalities. A set of intertemporal efficiency conditions (equilibrium conditions) yielding the optimal policy are given. By approximating the continuous problem by a set of discrete problems and appealing to a well known convergence theorem in functional analysis a continuous analog of the duality theorem is proved.

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Zusammenfassung Bei der Beschäftigung mit dynamischen Modellen der ökonomischen Politik stößt man auf Optimierungsprobleme, deren Zielfunktion ein Integral einer linearen Funktion von einer endlichen Anzahl stetiger Variablen ist und deren Beschränkungen lineare Integral-Ungleichungen sind. Eine Menge intertemporaler Effizienz-Bedingungen (Gleichgewichtsbedingungen), die zur optimalen Politik führen, sind gegeben. Durch Approximation des kontinuierlichen Problems mittels einer Menge von diskreten Problemen und Berufung auf einen wohlbekannten Konvergenzsatz aus der Funktionalanalysis wird ein stetiges Analogon des Dualitätstheorems bewiesen.

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The author is indebted to Mr.Arnold Faden for helpful suggestions and to ProfessorKarl A. Fox andGerhard Tintner for encouragement during the preparation of the paper. This research has been partially supported by a grant from the Ford Foundation to the School of Business Administration administered by the Center for Research in Management Science, University of California, Berkeley.

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Vorgel. v.:G. Tintner.     

Effect of stimulation rate on phoneme recognition by nucleus-22 cochlear implant listeners

This study investigated the effect of pulsatile stimulation rate on medial vowel and consonant recognition in cochlear implant listeners. Experiment 1 measured phoneme recognition as a function of stimulation rate in six Nucleus-22 cochlear implant listeners using an experimental four-channel continuous interleaved sampler (CIS) speech processing strategy. Results showed that all stimulation rates from 150 to 500 pulses/s/electrode produced equally good performance, while stimulation rates lower than 150 pulses/s/electrode produced significantly poorer performance. Experiment 2 measured phoneme recognition by implant listeners and normal-hearing listeners as a function of the low-pass cutoff frequency for envelope information. Results from both acoustic and electric hearing showed no significant difference in performance for all cutoff frequencies higher than 20 Hz. Both vowel and consonant scores dropped significantly when the cutoff frequency was reduced from 20 Hz to 2 Hz. The results of these two experiments suggest that temporal envelope information can be conveyed by relatively low stimulation rates. The pattern of results for both electrical and acoustic hearing is consistent with a simple model of temporal integration with an equivalent rectangular duration (ERD) of the temporal integrator of about 7 ms.     

Ein verallgemeinertes deterministisches Netzplanmodell

Zusammenfassung Bei der Netzplantechnik und ihren Anwendungen werden unterschiedliche Modelle und Verfahren behandelt. Unter Verwendung der Graphentheorie wird ein verallgemeinertes Netzplanmodell beschrieben, das die bekannten Modelle (Vorgangsknotennetzplan, Vorgangspfeilnetzplan, Ereignisknotennetzplan) als Sonderfälle enthält.

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Summary In network-analysis and its applications one usually distinguishes between activity-on-arrow, activity-on-node and event-on-node networks. Using the theory of graphs, a generalized deterministic network model is described, containing the well known techniques as special cases.

     

Maple packages for computing Hirota’s bilinear equation and multisoliton solutions of nonlinear evolution equations

The Hirota method for generating Hirota’s bilinear equation and constructing soliton solutions of nonlinear evolution equations is discussed and illustrated. Two Maple programs Bilinearization and Multisoliton are presented to automatically calculate Hirota’s bilinear equations for nonlinear evolution equations and to compute their N-soliton solutions for N = 1, 2 or 3, respectively. Different kinds of examples are used to demonstrate the effectiveness of the packages.     

Ground-based solar absorption studies for the Carbon Cycle science by Fourier Transform Spectroscopy (CC-FTS) mission

Carbon cycle science by Fourier transform spectroscopy (CC-FTS) is an advanced study for a future satellite mission. The goal of the mission is to obtain a better understanding of the carbon cycle in the Earth's atmosphere by monitoring total and partial columns of CO₂, CH₄, N₂O, and CO in the near infrared. CO₂, CH₄, and N₂O are important greenhouse gases, and CO is produced by incomplete combustion. The molecular O₂ column is also needed to obtain the effective optical path of the reflected sunlight and is used to normalize the column densities of the other gases. As part of this advanced study, ground-based Fourier transform spectra are used to evaluate the spectral region and resolution needed. Spectra in the 3950–7140 cm^?1 region with a spectral resolution of 0.0042 cm^?1 recorded at Kiruna (67.84°N, 20.41°E, and 419 m above sea level), Sweden, on 1 April 1998, were degraded to the resolutions of 0.01, 0.1, and 0.3 cm^?1. The effect of spectral resolution on the retrievals has been investigated with these four Kiruna spectra. To obtain further information on the spectral resolution, optical components and spectroscopic parameters required by the future mission, high-resolution solar absorption spectra between 2000 and 15000 cm^?1 were recorded using Fourier transform spectrometers at Kitt Peak (31.9°N, 111.6°W, and 2.1 km above sea level), Arizona, on 25 July 2005 and Waterloo (43.5°N, 80.6°W, and 0.3 km above sea level), Ontario, on 22 November 2006 with spectral resolutions of 0.01 and 0.1 cm^?1, respectively. Dry air volume mixing ratios (VMRs) of CO₂ and CH₄ were retrieved from these ground-based observations. The HITRAN 2004 spectroscopic parameters are used with the SFIT2 package for the spectral analysis. The measurement precisions for CO₂ and CH₄ total columns are better than 1.07% and 1.13%, respectively, for our observations. Based on these results, a Fourier transform spectrometer (maximum spectral resolution of 0.1 cm^?1 or 5 cm maximum optical path difference (MOPD)) operating between 2000 and 15000 cm^?1 is suggested as the primary instrument for the mission. Further progress in improving the atmospheric retrievals for CO₂, CH₄, and O₂ requires new laboratory measurements of the spectroscopic line parameters.     

Influence of different initial distributions on robust cooperation in scale-free networks: A comparative study

We study the evolutionary Prisoner's dilemma game on scale-free networks, focusing on the influence of different initial distributions for cooperators and defectors on the evolution of cooperation. To address this issue, we consider three types of initial distributions for defectors: uniform distribution at random, occupying the most connected nodes, and occupying the lowest-degree nodes, respectively. It is shown that initial configurations for defectors can crucially influence the cooperation level and the evolution speed of cooperation. Interestingly, the situation where defectors initially occupy the lowest-degree vertices can exhibit the most robust cooperation, compared with two other distributions. That is, the cooperation level is least affected by the initial percentage of defectors. Moreover, in this situation, the whole system evolves fastest to the prevalent cooperation. Besides, we obtain the critical values of initial frequency of defectors above which the extinction of cooperators occurs for the respective initial distributions. Our results might be helpful in explaining the maintenance of high cooperation in scale-free networks.