Abstract:
A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and predictive moments without the use of likelihood functions, prior densities and Bayes' Theorem. The posterior and predictive moments, based on a few relatively weak assumptions, are then used to obtain maximum entropy densities for parameters, realized error terms and future values of variables. Posterior means for parameters and realized error terms are shown to be equal to certain well known estimates and rationalized in terms of quadratic loss functions. Conditional maxent posterior densities for means and regression coefficients given scale parameters are in the normal form while scale parameters' maxent densities are in the exponential form. Marginal densities for individual regression coefficients, realized error terms and future values are in the Laplace or double-exponential form with heavier tails than normal densities with the same means and variances. It is concluded that these results will be very useful, particularly when there is difficulty in formulating appropriate likelihood functions and prior densities needed in traditional maximum likelihood and Bayesian approaches.

Abstract:
Let $G$ be a locally convex Lie group and $\pi:G \to \mathrm{U}(\mathcal{H})$ be a continuous unitary representation. $\pi$ is called smooth if the space of $\pi$-smooth vectors $\mathcal{H}^\infty\subset \mathcal{H}$ is dense. In this article we show that under certain conditions, concerning in particular the structure of the Lie algebra $\mathfrak{g}$ of $G$, a continuous unitary representation of $G$ is automatically smooth. As an application, this yields a dense space of smooth vectors for continuous positive energy representations of oscillator groups, double extensions of loop groups and the Virasoro group. Moreover we show the existence of a dense space of analytic vectors for the class of semibounded representations of Banach-Lie groups. Here $\pi$ is called semibounded, if $\pi$ is smooth and there exists a non-empty open subset $U\subset\mathfrak{g}$ such that the operators $i\mathrm{d}\pi(x)$ from the derived representation are uniformly bounded from above for $x\in U$.

Abstract:
An oscillator group $G$ is a semidirect product of a Heisenberg group with a one-parameter group. In this article we construct Olshanski semigroups for infinite-dimensional oscillator groups. These are complex involutive semigroups which have a polar decomposition. The main application will be for representations $\pi$ of $G$ which are semibounded, i.e., there exists a non-empty open subset $U$ of the Lie algebra $\mathfrak{g}$ such that the operators $id\pi(x)$ from the derived representation are uniformly bounded from above for $x\in U$. More precisely we show that every semibounded representation of an oscillator group $G$ extends to a non-degenerate holomorphic representation of such a semigroup and conversely each non-degenerate holomorphic representation of such a semigroup gives rise to a semibounded representation of $G$. The main application of this result is a classification of representations of the canonical commutation relations with a positive Hamiltonian, which will be obtained in a subsequent paper. Moreover it yields direct integral decomposition into irreducible ones and implies the existence of a dense subspace of analytic vectors for semibounded representations of $G$.

Abstract:
Recent discussions on high-speed civil transport (HSCT) systems have renewed the interest in the chemistry of supersonic-aircraft plumes. The engines of these aircraft emit large concentrations of radicals like O, H, OH, and NO. In order to study the effect of these species on the composition of the atmosphere, the detailed chemistry of an expanding and cooling plume is examined for different expansion models. For a representative flight at 26 km the computed trace gas concentrations do not differ significantly for different models of the expansion behaviour. However, it is shown that the distributions predicted by all these models differ significantly from those adopted in conventional meso-scale and global models in which the plume chemistry is not treated in detail. This applies in particular to the reservoir species HONO and H2O2.

Abstract:
To elaborate stratospheric ozone depletion processes, measurements of diffusion coefficients of selected gas phase molecules (i.e. HCl, CH3OH, HCOOH and CH3COOH; Katsambas et al., 1997; Kondratyev and Varotsos, 1996; Varotsos et al., 1994, 1995) in ice in the temperature range 170–195 K have been analyzed with respect to the mechanisms and rates of diffusion. It is argued that the diffusion in ice of these compounds is governed by a vacancy – mediated mechanism, i.e. H2O vacancies are required to diffuse to lattice sites adjacent to these compounds prior to the diffusion of the corresponding molecule into the vacancy sites. In addition, we show that the diffusion coefficients of these compounds exhibit a specific interconnection, i.e. a linear relationship holds between the logarithm of the pre-exponential factor, Do, and the activation energy E. The physical meaning of this interconnection is discussed.

Abstract:
It was examined how much speech material is required to build a prosodic model for duration, fundamental frequency and intensity. For each of two speakers, fifty multiple linear regression models were built on the basis of seventy utterances per speaker (7'522 and 7'643 segments respectively). Models based on eight and twenty utterances showed good stability, satisfactory prediction for novel material, as well as closeness of fits comparable to those reported by other researchers for much larger corpora. Linear regressions were typically based on about ten independent predictors per prosodic parameter, which had previously been ranked according to their prediction of the dependent parameter. This ranking procedure advantageously replaced more commonly used regression trees. Variation in the closeness of fit of models based on sliding windows eight and twenty utterances long were traced to variations in bias, i.e., in the degree to which models systematically under- or overestimate target values. While the models in this study involved simple, non-optimized linear regressions without interactions, avenues are suggested for further improving the performance of this class of models. The results of this study suggest that a series of well-adapted small-footprint models provide more accurate information about the individual use of prosody in specific speech situations than a single model based on abundant data.

Abstract:
To elaborate stratospheric ozone depletion processes, measurements of diffusion coefficients of selected gas phase molecules (i.e. HCl, CH3OH, HCOOH and CH3COOH) in ice in the temperature range 170–195 K have been analyzed with respect to the mechanisms and rates of diffusion. It is argued that the diffusion in ice of these compounds is governed by a vacancy – mediated mechanism, i.e. H2O vacancies are required to diffuse to lattice sites adjacent to these compounds prior to the diffusion of the corresponding molecule into the vacancy sites. In addition, we show that the diffusion coefficients of these compounds exhibit a specific interconnection, i.e. a linear relationship holds between the logarithm of the pre-exponential factor, Do, and the activation energy E. The physical meaning of this interconnection is discussed.

Abstract:
This study investigated school administrators’ perceptions of school improvement policies in a high-impact policy environment by measuring the impact of accountability, site-based management, professional development, and scheduling reform on the three dependent variables of a) academic outcomes, b) staff morale, and c) parent and community involvement. Using a convenience sampling method, 49 public school principals from Texas participated and an online survey was constructed to gather both quantitative (i.e., Likert scale) and qualitative (i.e., open ended response) data. The findings clearly point to principals, regardless of geographical district type and grade level school type, viewing less controversial and more intrinsically oriented policies (i.e., site-based management and professional development) as having a greater positive impact on outcomes as a whole than more radical alternatives (i.e., accountability and time and schedule reform). The evidence suggests that more aggressive school improvement policy approaches are likely failing to generate enough convincing outcomes to generate high commitment and confidence from school leaders. Further studies may look at the interaction of policy impact with minority student enrollments and with subgroup populations.