Vibrational spectroscopic study of budesonide

The Raman spectrum of budesonide is reported for the first time, and molecular assignments are proposed on the basis of ab initio BLYP DFT calculations with a 6‐31 G* basis set and vibrational wavenumbers predicted on a quasi‐harmonic approximation. Comparison with previously published infrared data has explained several spectral features, and the relative band intensities in the CO and CC stretching regions are interpreted. The results from this study provide data that can be used for the preparative process monitoring of budesonide, an important steroidal pharmaceutical in various dosage forms, and its interaction with excipients and other components. Copyright © 2007 John Wiley & Sons, Ltd.     

Mathematical foundations of quantum field theory: Fermions,gauge fields,and supersymmetry part I: Lattice field theories

In this paper we explore the mathematical foundations of quantum field theory. From the mathematical point of view, quantum field theory involves several revolutions in structure just as severe as, if not more than, the revolutionary change involved in the move from classical to quantum mechanics. Ordinary quantum mechanics is based upon real-valued observables which are not all compatible. We will see that the proper mathematical understanding of Fermi fields involves a new concept of probability theory, the graded probability space. This new concept also yields new points of view concerning ergodic theorems in statistical mechanics.     

Some Experiences with the Teaching of Decision Support Systems to Management Students

There are essentially two schools of thought regarding the function of decision support systems. One is that the main purpose is to support the decision-maker in whatever style of decision-making he or she wishes. The other is that the support, while suiting the decision-maker's individual style, must also be based on an appropriate theoretical paradigm. The work with students of decision support systems reported here suggests that the latter, normative, view is not one which comes naturally to many of the students, even when working on an example where it seemed relatively easy to incorporate. Other conclusions are also presented, relating to the choice of software for decision support system development, the process of teaching about decision support systems, and group formation.     

Molecular structure and puckering potential of gas-phase 1-pyrroline as determined by microwave and infrared spectroscopy

The microwave spectrum of 1-pyrroline has been measured from 8 to 48 GHz. The transitions have been assigned to those of the ground state and the four lowest excited states of the ring-puckering vibration of monomer, which is a five-membered ring molecule with one CN double bond. The trimer, which exists in the liquid phase, has not been detected in the gas phase. The geometrical structure of the monomer has been estimated by an ab initio calculation and the trimer by a molecular mechanics calculation. The former is consistent with the experimental rotational constants. A gas-phase infrared spectrum has also been measured, and the ring-puckering potential has been determined by an analysis of the combination bands of the ring-puckering mode and the ring-stretching modes. The potential is described using a puckering coordinate, z, as V(z) = az² + bz⁴, where $\text{a = ?3.358(16) × 10}{}^4\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^{\mathrm{?2}}$ and $\text{b = 1.345(9) × 10}{}^6\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^{\mathrm{?4}}$; these values are intermediate of the corresponding values for cyclopentene and 1-pyrazoline. The nuclear quadrupole coupling constants, χ_aa = ?4.39(10), χ_bb = 1.04(10), and χ_cc = 3.35(10) MHz, have been determined by an analysis of well-resolved hyperfine splittings. These constants have been reproduced by an ab initio calculation with a 4-31G(N¹) basis set.     

Multi-grid Monte Carlo (III). Two-dimensional O(4)-symmetric non-linear σ-model

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear σ-model [ = SU(2) principal chirral model]], on lattices up to 256×256. We find a dynamic critical exponent for the W-cycle and for the V-cycle, compared to for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a 256×256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.