On the non-existence of a rationality definition for extensive games

Standard solution concepts, like subgame perfection, implicitly require that players will continue to assume everybody is rational even if this has been revealed to be false by virtue of having reached a node that could not have been reached had all players behaved rationally. Several attempts have been made in the literature to solve this problem. The present paper shows that the problem is insoluble.     

Multivariate Exponential Distributions with Constant Failure Rates

In this paper a multivariate failure rate representation based on Cox's conditional failure rate is introduced, characterizations of the Freund–Block and the Marshall–Olkin multivariate exponential distributions are obtained, and generalizations of the Block–Basu and the Friday–Patil bivariate exponential distributions are proposed.     

Effects of circuit loss and space charge in gyro-travelling-wave tubes

A modified dispersion relation of a gyro-TWT using a cylindrical waveguide excited in aT E _mn -mode is derived incorporating the effect of the transverse space charge forces. The relation is subsequently studied considering the circuit losses and interpreted for the conventional TWT-type gain equation. The second harmonic operation using theT E ₀₂ cylindrical waveguide mode resonated with the second beam-harmonic mode is found to be more sensitive to the Pierce's loss and space-charge parameters for a gyro-TWT than the fundamental operation using theT E ₀₁ cylindrical waveguide mode resonated with the first beam-harmonic mode. It is established that these parameters substantially influence the device gain and must be considered for the prediction of its accurate value. Furthermore, these parameters when properly controlled can also improve the device bandwidth.     

Deformation of a planar sinusoidal elastic beam

Summary The load-deformation curves of sinusoidal shaped elastic beams under tensile end loads with and without distributed loading along the beam proportional to the local displacements have been determined.

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Zusammenfassung Die Last-Verformungskurven von sinusförmigen elastischen Balken mit Endnormalkräften, mit und ohne Streckenlast entlang des Balkens proportional zu den örtlichen Verformungen, sind bestimmt worden.

     

Total ionization cross section in electron-hydrogen scattering

The total ionization cross section in electron-hydrogen scattering in the energy range 20.4–68.0 eV has been calculated by a method in which the initial state of the system is treated by a distorted wave polarized orbital method and the final state is described by (1) a product of two unscreened Coulomb functions and (2) a product of a plane wave and a Coulomb function. The corresponding two sets of results using a plane wave in the incident channel have also been reported. The present results where both the electrons are represented by Coulomb waves are in closer agreement than other theoretical predictions With measured values.     

Impact parameter study in multiparticle production at 70 GeV/c

This paper presents a study of the experimental lower boundb _L, on the root-mean-squared impact parameter of the multiparticle production in 70 GeV/c p-nucleon interaction. It has been observed that theb _L decreases with increasing final state multiplicity (n) at this fixed energy. The results are in good agreement with those of other authors.The authors would like to thank Prof. K. D. Tolostov of Dubna, U.S.S.R. for kindly supplying the exposed emulsion plates.     

Time-resolved electron spin resonance with electron spin polarization (CIDEP) as a sensitive probe of degenerate electron exchange reactions

It is shown that the occurrence of electron-exchange processes produces a distinctive effect in the time-resolved electron spin resonance spectra of spin-polarized radicals observed in the continuous presence of a microwave field. The effects observed are consistent with a theory based upon the Bloch equations.     

Spot Size Technique: A Theoretical Approach To Optimize Dispersion Compensated

Using a spot size based optimization technique, a bend loss versus dispersion diagram has been obtained theoretically for the most widely used step-index disper sion compensated optical fibers (DCF). The Rayleigh scattering loss can be incorpo rated with bend loss to calculate figure of merit (FOM), thus giving an FOM versus dispersion curve on a single diagram. The plot of the FOM-dispersion curve on a single diagram is useful from the designer's point of view, as it provides a quick reference for choosing the best suitable DCF, which should have large negative dispersion as well as maximum possible value of FOM. The effect of fiber manufac turing losses such as absorption loss on the maximum value of FOM has also been estimated.     

Synthesis,reduction, and reductive alkylation of a few tricyclic α,β-unsaturated ketones

Reduction and reductive alkylation of the tricyclic α,β-unsaturated ketones 9–12 afforded the saturated ketones 13–21 in high yields.     

Identifiability of the multinormal and other distributions under competing risks model

Let X₁, X₂ ,…, X_p be p random variables with joint distribution function F(x₁ ,…, x_p). Let Z = min(X₁, X₂ ,…, X_p) and I = i if Z = X_i. In this paper the problem of identifying the distribution function F(x₁ ,…, x_p), given the distribution Z or that of the identified minimum (Z, I), has been considered when F is a multivariate normal distribution. For the case p = 2, the problem is completely solved. If p = 3 and the distribution of (Z, I) is given, we get a partial solution allowing us to identify the independent case. These results seem to be highly nontrivial and depend upon Liouville's result that the (univariate) normal distribution function is a nonelementary function. Some other examples are given including the bivariate exponential distribution of Marshall and Olkin, Gumbel, and the absolutely continuous bivariate exponential extension of Block and Basu.