Millimeterwave spectra of some superionic conductors

Using a quasi-optical continuously tunable spectrometer in the frequency range of 40–90 GHz (=7.5-3.3 mm) the absorption spectra of the superionic conductors Na-alumina, Ag-alumina,-AgI and CuTeBr have been measured at various temperatures. In the measured spectral range all the materials showed a monotonic increase in the absorption as a function of frequency. These results are discussed in the light of existing theoretical models.Alfred P. Sloan Foundation Fellow     

Adiabatic behavior of sine-Gordon solitons in the presence of perturbations

The behavior of sine-Gordon solitons in the presence of weak perturbations is considered. The procedure is based on the exact inverse scattering solution of the unperturbed sine-Gordon equation. Accounting for perturbations such as those arising from impurities, external forces as well damping and spatially inhomogeneous frequencies the corresponding perturbed operator equation can be solved by the Green's function technique if one expands the Green's operator in terms of a set of biorthogonal eigenfunctions. Ordinary linear differential equations prescribing the time evolution of the scattering data are obtained. Instead of solving the inverse scattering problem completely the adiabatic assumption is then used anticipating the result that solitons maintain their integrity to a high degree. Explicit solutions for the one-soliton dynamics are presented.Work supported by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich Nr. 162 Plasmaphysik Bochum/Jülich     

Some remarks concerning the M.I.T. public-key cryptosystem

Let a messageM be encrypted by raisingM to a powere moduloR, whereR ande are integers which are made public. The recipient of this encrypted form ofM can decipher it by raising the cipher text to a powerd moduloR. Only the recipient knows the values of the two large primesp ₁,p ₂ such thatR=p ₁ p ₂; consequently, only he knowsd, ase is preselected such that (e, (p ₁ – 1)(p ₂ – 1))=1 anded 1 (mod (p ₁ – 1)(p ₂ – 1)).Recently several attacks have been made on the proposed security of this cryptosystem under iteration of the encryption procedure. In this paper we discuss methods of selecting the primesp ₁,p ₂ and the encryption exponente such that the possibility of breaking this cryptosystem by using an iteration procedure is minimized. Several numerical results are also presented.     

Smooth distribution group and Schrödinger equation in Lp(Rn)

In College de France, Seminaire E.D.P. II, Nov. 1963–May 1964, Peetre has introduced the smooth distribution semi-group which is discussed here. This notion is redefined by introducing a functional space $\text{T}$, which measures the regularity of such a distribution. This allows us to give a spectral characterization of such groups. We show that the iterated resolvent of the infinitesimal generator of a smooth distribution group satisfies the relation

$\text{6(λ?A)}{}^{\mathrm{?q}}\text{6L(X)?cq}{}^{\mathrm{k}}\text{|λ|}{}^{\mathrm{k}}\text{|}$

, Re λ ≠ 0. The application of this notion is illustrated by the study of the Schrödinger equation in L^p($\text{R}$ⁿ).     

A method of bisection for discounted Markov decision problems

We describe in this paper how to introduce the concept of bisection into Dynamic Programming of stationary Markovian decision processes with infinite horizon. The combination of these two methods delivers a new class of algorithms. A basic bisection algorithm is given. Its rate of convergence is rather independent of the input data, especially the discount factor or contracting factor. If in any method of successive approximations we have > 0.5, then the bisection method has a faster convergence than the successive approximations. Bisection is especially advantageous if is close to unity. The computation of two inventory control problems with the basic algorithm of bisection is presented. The second example has a discount factor=0.9994. Using Howard's automobile replacement problem the new method is compared with value iteration, policy iteration andPorteus' method of extrapolations. Among them bisection turned out to be the most powerful procedure. The combination withPorteus' method of extrapolation is not as efficient as the bisection method alone. We also investigate how to combine the bisection method with monotone extrapolation when the transition matrices do not have equal row sums.

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Zusammenfassung In dieser Arbeit wird die Idee der Bisektion in die Dynamische Optimierung stationärer Markovscher Entscheidungsprozesse mit unendlichem Planungshorizont eingeführt. Die Verbindung dieser beiden Methoden schafft eine neue Klasse von Algorithmen. Ein Basisalgorithmus, der selbst Ausgangspunkt zahlreicher Verfeinerungen und Spezialisierungen bildet, wird vorgestellt. Seine Konvergenzgeschwindigkeit ist nahezu unabhängig von Input-Daten, speziell dem Diskontfaktor bzw. der Lipschitz-Konstanten. Die Bisektion ist immer dann schneller als die Methode der sukzessiven Approximation, falls>0,5 ist. Deshalb ist das neue Verfahren besonders bei Problemen mit schwacher Kontraktionseigenschaft, d.h. nahe bei eins, geeignet. Der Rechenverlauf des Basisalgorithmus wird anhand zweier Lagerhaltungsmodelle diskutiert von denen das zweite eine Lipschitz-Konstante=0.9994 besitzt. Am Beispiel des Howardschen Autoersatzproblems zeigt sich, daß das Bisektionsverfahren im Vergleich mit der Wertiteration, Politikiteration undPorteus' Extrapolationsverfahren das schnellste Verfahren ist. Die Kombination der Bisektion mit der Extrapolationsmethode ist ungünstiger als die Bisektion allein. Es wird noch untersucht, wie die Bisektion mit der monotonen Extrapolation verbunden werden kann, wenn die Zustands-übergangsmatrizen keine konstanten Zeilensummen besitzen.

     

A comparison of two approaches to the optimal positioning of a new product in an attribute space

This paper is concerned with the optimal positioning of a new product in an attribute space. A deterministic optimization model that relies on the axiom of choice is compared with the model byShocker/Srinivasan [1974] that incorporates a probabilistic measure of choice. Investigating the assumptions and the construction of both models, it is shown that the probability function byShocker/Srinivasan is based on a controversial assumption and incorporates a parameter that has not been given an economic explanation. Furthermore, both models are applied to complex configurations. It is demonstrated that the optimal positions for the new product resulting from the model byShocker/Srinivasan depend heavily on the parameter just mentioned and may run contrary to plausible consequences of the axiom of choice.

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Zusammenfassung Für die optimale Gestaltung neuer Produkte, d.h. ihrer Positionierung in einem Raum von Produkteigenschaften, wird ein Modell angeboten, das auf einer deterministischen Kaufentscheidung beruht, ein anderes, das eine stochastische Kaufentscheidung unterstellt. Es wird gezeigt, daß der zuletzt genannte Modelltyp stark von der Spezifikation eines ökonomisch bisher nicht erklärten Parameters abhängt und z.T. Konsequenzen aufweist, die dem Wahlaxiom zuwider laufen, auf das das erstgenannte Modell aufbaut. Durch einen Vergleich auch komplexer Konfigurationen von Käuferbeurteilungen neuer Produkte wird gezeigt, welche Gestaltungsentscheidungen auf der Grundlage der beiden Modelle zur Optimierung einer Zielfunktion zu treffen sind.

     

Über die optimale Beleuchtung einer geraden Straße

The following problem is due toL. Fejes Tóth: For a given sort of lamps letf(x) be the intensity of brightness in each point having distancex from the foot of the lamp. How must infinitely many lamps of this kind be arranged on a both-side infinite rectilinear road, such that the infimum of the intensities of brightness, extended over the whole street, is maximal, subject to the condition that the average number of lamps per kilometer is bounded by a fixed number (“Best distributions”)? The main result of this paper is: Iff is strictly convex, the equidistant distribution is best.     

Eine spezielle Vorgangsdauerverteilung zur Netzplananalyse durch Simulation

Zusammenfassung Es wird eineC genannte Verteilung bereitgestellt, die sich zur Erfassung von Vorgangsdauern bei Netzplanproblemen eignet und durch besondere Wirtschaftlichkeit bei Simulationsmethoden auszeichnet.

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Summary In this paper a distributionC will be presented for the activity duration times in network problems which from the economical point of view is fit for the solution to network problems via Monte Carlo simulation.

     

Numerical Integration of Systems of Stiff Ordinary Differential Equations with Special Structure

Algorithms for the solution of general systems of stiff differentialequations commonly use implicit integration formulae. The associatednon-linear equations at each step of the integration are efficientlysolved by an iteration such as the parallel chord method, wherethe matrix is an approximation for the Jacobian at a calculatedpoint of the solution. This iteration frequently gives sufficientlyrapid convergence over a number of integration steps beforeupdating and re-inversion of the matrix is required. When thedifferential equations have a special structure, satisfactoryconvergence may be maintained by updating a partition of theJacobian less frequently than the remainder and an efficientcomputational procedure consists in calculating the correspondingupdate of the inverse. Sufficient conditions for local convergencemay be expressed in terms of the difference between the iterationmatrix and the derivative at the solution or in terms of thedifference of the corresponding inverses. Similarly the asymptoticrate of convergence is estimated in terms of the norms of theseperturbations. To assess the effectiveness of updating a partitionof the Jacobian or its inverse we set the corresponding perturbationto zero and evaluate the estimate of the rate of convergence.Variable transformation and "weighting" of equations may beused to obtain more accurate computable estimates of convergencerates and tighter conditions for convergence. This is particularlyrelevant in non-linear stiff systems arising in applicationsfrom physics, chemistry and engineering and associated withfast and slow motions. Such systems exhibit special structurein the Jacobian and higher derivatives related to the sensitivityof the system to the components of the fast motion which makesthem particularly amenable to matrix updating techniques. Anumber of illustrative problems from the literature are cited.A worked example has been solved numerically using an inversewhose partitions are updated irregularly as required for convergenceand a comparison is made of iteration counts and inversion statisticswith updating of the full inverse. Computational savings maysometimes belarge.     

Electron tunneling into ion implanted PbMn and SnMn alloys

Tunnel junctions ofPb-I-Al andSn-I-Al were implanted at low temperatures with Mn ions in the ppm region. The tunnel characteristicdI/dV was measured on the pure sample and on the alloy with different concentrations. A bound state is found in both systems at an energy 0.7 ₀. Comparison with theory confirms, that the Kondo effect is not necessary for the existence of a bound state.