Necessary conditions for normed convergence of critical multitype Bienaymé-Galton-Watson processes without variance

The condition on the offspring distribution in the critical multitype Bienaymé-Galton-Watson process without variance, which was previously shown to be sufficient for the existence of the analogue of the exponential limit law, is now shown also to be necessary. This completely extends previous one-type work of R. S. Slack.     

Bemerkungen zu einem Rundungsproblem bei der Lagerhaltung

Zusammenfassung Bei der Auffüllung eines Lagers treten in der Praxis häufig Rundungen auf, die etwa durch Abweichungen des errechneten Bedarfs von der lieferbaren Menge entstehen können und die nicht immer von vornherein vernachlässigt werden dürfen. Es werden innerhalb eines speziellen Modells u. a. die entstehenden mittleren Abweichungen ermittelt und für drei Beispiele einige der interessierenden Größen angegeben.

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Summary Frequently in practice it is not possible to order just the quantities, which are needed to meet the demand; for instance the calculated requirements are not identical to the quantities actually available for consignment. Sometimes these deviations cannot be neglected. This paper investigates some aspects of this problem. The mean deviation and some other interesting quantities are determined for a special model and they are given explicitly for three examples.

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Vorgel. v.:J. Nitsche.     

Verification of the optimal probabilistic basis of aural processing in pitch of complex tones

Periodicity pitch for complex tones has been quantitatively accounted for by a two-stage process of Fourier-frequency analysis subject to random errors and significant nonlinearities, followed by an harmonic pattern recognizer that makes an optimum probabilistic estimate of the fundamental period of musical and speech sounds. The theory predicts that periodicity pitch is a multimodal probabilistic function of a given stimulus. A clear and empirically supported distinction is made between limitations on the pitch mechanism caused by the stochastic nature of aural frequency representation and by the deterministic resolution bandwidths of aural frequency analysis. This model was developed earlier [J. L. Goldstein, J. Acoust. Soc. Am 54, 1496-1516 (1973)] to account for probabilistic data on pitch errors [A. J. M. Houtsma and J. L. Goldstein, J. Acoust. Soc. Am. 51, 520 (1972)] measured with periodic stimuli comprising two successive harmonics. This paper presents new predictions by the theory that were calculated, with computer simulation where needed, for known probabilistic pitch data from stimuli comprising three to six successive harmonics. Predicted pitch errors increase with increasing errors in estimating the frequencies of stimulus harmonics and decrease as more harmonics are added to the stimulus. Optimum processor theory fully accounts for the multicomponent pitch data on the basis of similar errors in estimating component stimulus frequencies as reported earlier, thus providing further evidence for the optimum probabilistic basis of aural signal processing in pitch of complex tones.     

Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit

Equivalence (allowing for convex combinations) of microcanonical, canonical and grandcanonical ensembles for states of classical systems is established under very mild assumptions on the limiting state. We introduce the notion of conditional equilibrium (C.E.), a property of states of infinite systems which characterizes convex combinations of limits of microcanonical ensembles. It is shown that C.E. states are, under quite general conditions, mixtures of Gibbs states.Supported in part by NSF Grant No. MCS 75-21684 A02Supported in part by NSF Grant No. MPS 72-04534Supported in part by NSF Grant No. Phy 77-22302     

High resolution C nuclear magnetic resonance spectra for symmetrical orthodihalobenzenes including long-range CH couplings

Analysis of high resolution ¹³C NMR spectra for symmetrical orthodihalobenzenes have provided all long-range ¹³CH coupling values in orthodichloro-, dibromo-, and diiodobenzene. Furthermore, since the analyses were sensitive to the sign of the coupling constants, the relative signs of these long-range ¹³CH couplings have been determined from unique spectral fits. The substituent effects on the chemical shifts in this series of compounds appear to be additive. The ¹³CH couplings are compared with coupling values in other compounds and are shown to be related to substituent electronegativity. The absolute magnitude of the ¹³CH couplings for these halogen-substituted compounds are larger than those observed in benzene, with but one exception. In all cases, three-bonded ¹³CH couplings are found to be larger than the two-bond values.     

Cross sections at “asymptotic” energies in thep¯p collider

As a whole new range of energies will be soon experimentally studied, we present predictions for hadronic cross sections at future very high energy accelerators. All calculations are based on results accumulated in reggeon field theory, where methods of field theory (in the continuum and on the lattice) and statistical mechanics have been used. We have employed these results and translated them into a manageable phenomenological analysis of existing FERMILAB-ISR data. The size of the non-leading terms is determined and enables us to predict cross sections at energies in the range of the near futurep¯p collider. Parameter-free scaling functions and critical exponents which are exactly calculable in RFT are thus brought to an experimental test.     

Coiling, entrainment, and hydrodynamic coupling of decelerated fluid jets

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.     

Boltzmann entropy for dense fluids not in local equilibrium

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f=[f(x,v)] and the total energy E. We find that S(f(t),E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(M(t))=S(M(X(t))) should hold generally for "typical" (the overwhelming majority of) initial microstates (phase points) X0 belonging to the initial macrostate M0, satisfying M(X0)=M(0). This is a consequence of Liouville's theorem when M(t) evolves according to an autonomous deterministic law.