Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440–464) introduced a class of multinomial goodness-of-fit statistics R^a based on power divergence. All R^a have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of R^a under local alternatives. We obtain an expression of approximation for the distribution of R^a under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of R^a. We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of R^a. We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance.     

Weak Gibbs Measures for Intermittent Systems and Weakly Gibbsian States in Statistical Mechanics

In this paper, we associate weak Gibbs measures for intermittent maps with non-Gibbsian weakly Gibbsian states in statistical mechanics in the sense of Dobrushin [4, 5]. We show a higher dimensional intermittent map of which the Sinai-Bowen-Ruelle measure is a weak Gibbs equilibrium state and a weakly Gibbsian state in the sense of Dobrushin admitting essential discontinuities in its conditional probabilities.     

Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points

We consider Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients onL ^p (,w) where 1<p<,w is a Muckenhoupt weight and belongs to a large class of Carleson curves. This class includes curves with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. Our main result says that the essential spectrum of a Toeplitz operator is obtained from the essential range of its symbol by joining the endpoints of each jump by a certain spiralic horn, which may degenerate to a usual horn, a logarithmic spiral, a circular arc or a line segment if the curve and the weightw behave sufficiently well at the point where the symbol has a jump. This result implies a symbol calculus for the closed algebra of singular integral operators with piecewise continuous coefficients onL ^p (,w).Research supported by the Alfried Krupp Förderpreis für junge Hochschullehrer of the Krupp Foundation.     

A variational principle for transition and density matrices and approximations to the equations-of-motion

A general variational principle for transition and density matrices is proposed. The principle is closely related to Rowe's variational treatment of the equations-of-motion method. It permits the simultaneous construction of coupled approximations for two eigenstates, and it is a straightforward extension of the usual variational method.     

Study of the electronic structure of radicals by the CI method

Results are presented which were obtained in the -electronic approximation for the ground state properties of the benzyl radical (total energy, distribution of the electronic and spin density) by the CI method on closed and open shell SCF orbitals taking into account all singly and some doubly excited configurations. Some of the singly excited configurations which in the first order perturbation theory do not interact with the ground state configuration contribute to the ground state more than some of those which interact with the latter. Certain doubly excited configurations contribute more than some singly ones. The consideration of all singly excited configurations leads to a lower ground state energy if the closed shell orbitals are used compared with the open shell ones. The former bring about the non-uniform electron density distribution becoming more smooth as the set of the basis configurations becomes larger. The spin density distribution strongly depends on the number of the configurations as well as on the orbitals used for their construction. The computation of the benzyl radical done by Hinchliffe by the CI method on open shell orbitals is believed to be wrong.

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Zusammenfassung Rechnungen im Rahmen der -Elektronen-NÄherung für den Grundzustand des Benzyl-Radikals (Gesamtenergie, Verteilung von Elektronen- und Spin-Dichte) mittels des SCF-CI-Verfahrens für geschlossene und offene Schalen unter Einschlu\ aller einfach und einiger zweifach angeregten Konfigurationen werden mitgeteilt. Dabei zeigt sich, da\ einfach angeregte Konfigurationen, die in der Störungsrechnung erster Ordnung nicht mit der Grundfiguration kombinieren, zum Grundzustand mehr als solche, die kombinieren, beitragen.Zusammenfassung Die Berücksichtigung aller einfach angeregten Konfigurationen führt zu einer niedrigeren Grundzustandsenergie, wenn die Einteilchenfunktionen, die sich für geschlossene Schalen ergeben, an Stelle derer für offene Schalen verwendet werden. Erstere führen zu ungleichförmiger Verteilung der Elektronendichte, die um so mehr geglÄttet ist, je grö\er die Anzahl der Konfigurationen wird. Die Verteilung der Spin-Dichte hÄngt stark von der Anzahl der Konfigurationen wie auch von den benutzten Orbitalen ab. Die Berechnung des Benzyl-Radikals von Hinchliffe mittels des CI-Verfahrens für offene Schalen wird als unrichtig angesehen.

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Résumé Propriétés de l'état fondamental du radical benzyle (énergie totale, distribution des densités électroniques et de spin) dans l'approximation par la méthode d'I.C. sur les orbitales SCF des couches complètes et incomplètes avec introduction de toutes les configurations monoexcitées et de certaines configurations diexcitées. Certaines configurations monoexcitées qui n'intéragissent pas avec la configuration fondamentale au premier ordre de la théorie des perturbations apportent à l'état fondamental une contribution plus élevée que certains de ceux qui interagissent à ce stade là. Certaines configurations diexcitées ont une contribution plus forte que certaines monoexcitées. Si l'on tient compte de toutes les configurations monoexcitées, on obtient une énergie plus basse en utilisant les orbitales des couches complètes et non celles des couches ouvertes. On obtient ainsi une distribution électronique dont la non uniformité va en s'affaiblissant lorsque la base de configurations s'élargit. La distribution de densité de spin dépend fortement du nombre de configurations employé ainsi que des orbitales utilisées. Le calcul d'I.C. d'Hinchliffe sur le radical benzyle à l'aide des orbitales des couches ouvertes semble faux.

     

Comparison of the hole mobility in undoped and boron-doped polycrystalline CVD diamond films

The drift mobility of nonequilibrium holes injected in undoped polycrystalline diamond films was determined, by a transit-time technique, as ca. 10⁻³ cm²/(V s). This hole mobility is three orders of magnitude lower than the “equilibrium” mobility in boron-doped diamond films [0.1–1 cm²/(V s)], determined from the films' dc conductivity. This difference is explained by the effect of a nonequilibrium charge carrier trapping during the carrier transport in polycrystalline diamond. Received: 3 December 1997 / Accepted: 9 April 1998     

Electron-nuclear correlations for photo-induced dynamics in molecular dimers

Ultrafast photoinduced dynamics of electronic excitation in molecular dimers is drastically affected by the dynamic reorganization of inter- and intra- molecular nuclear configuration modeled by a quantized nuclear degree of freedom. The dynamics of the electronic population and nuclear coherence is analyzed by solving the chain of coupled differential equations for population inversion, electron-vibrational correlation, etc. Intriguing results are obtained in the approximation of a small change of the nuclear equilibrium upon photoexcitation. In the limiting case of resonance between the electronic energy gap and the frequency of the nuclear mode these results are justified by comparison to the exactly solvable Jaynes-Cummings model. It is found that the photoinduced processes in the model dimer are arranged according to their time scales: (i) Fast scale of nuclear motion, (ii) intermediate scale of dynamical redistribution of electronic population between excited states as well as growth and dynamics of electron-nuclear correlation, (iii) slow scale of electronic population approach to the quasi-equilibrium distribution, decay of electron-nuclear correlation, and decrease of the amplitude of mean coordinate oscillation. The latter processes are accompanied by a noticeable growth of the nuclear coordinate dispersion associated with the overall nuclear wave packet width. The demonstrated quantum relaxation features of the photoinduced vibronic dynamics in molecular dimers are obtained by a simple method, applicable to systems with many degrees of freedom.