Quantum Ising-like spin-j model with multipole-multipole interactions: Second order mean-field approach

A quantum Ising-like spin-j model, characterized by arbitrary multipole-multipole interactions as well as external fields, is proposed and analyzed. A thorough discussion of the algebraic properties of the dynamical variables (which belong to SU(2j+1)) is performed, whereby by the application of an improved version of the mean-field theory (which has the usual mean-field theory as its zeroeth order approximation) an explicit expression for the free energy is derived.     

Distortion theorems for locally univalent Bloch functions

A holomorphic functionf defined on the unit disk d is called a Bloch function provided {fx73-02} For α ∃ (0,1] letB∞(α)denote the class of locally univalent Bloch functionsf normalized by ∥f∥_B ≤1f(0) = 0 andf’(0) = α. A type of subordination theorem is established for B∞(α). This subordination theorem is used to derive sharp growth, distortion, curvature and covering theorems for B∞(α). Supported as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation. Research supported in part by a National Science Foundation grant.     

Effective energy coupling for 200-Mhz pulsed radiofrequency spectroscopic discharges

The introduction of various new radiofrequency electrical discharges has placed increased emphasis on circuit design which provides optimal energy transfer between a generator and its corresponding spectroscopic “load”. This technology is well developed for high-frequency (ca. 27 MHz) inductively-coupled plasma discharges and for cavity discharges which operate in the microwave region (e.g., 2450 MHz). The 200-MHz very high frequency (VHF) region has received less attention. New circuitry is described which allows effective transfer of high power (5-kW), pulsed (2.5-μs), VHF (200-MHz) energy into a plasma suitable for analytical purposes. A triple-stub tuner is used in this circuitry. Comparison with other approaches and applicability to a variety of discharge systems are discussed.     

Competitive systems with stage structure of distributed-delay type

This paper considers a delay differential equation model for the interaction among n species, the adult members of which are in competition. For each of the n species the model incorporates an infinite distributed time delay which represents the time from birth to maturity of that species. Thus, the time delays appear in the adult recruitment terms. The dynamics of the model are determined, and sharp global stability criteria are established for the interior equilibrium as well as the axial equilibrium.     

O–O2 state-to-state vibrational relaxation and dissociation rates based on quasiclassical calculations

A complete set of V–T (vibration–translation) relaxation rates and of dissociation coefficients for the system O–O₂ have been obtained by using quasiclassical trajectories on the Varandas and Pais potential energy surface. The results, averaged on a Boltzmann rotational distribution, cover the whole range of the vibrational ladder and are reproduced in closed form ready to be implemented in state-to-state kinetic models. The accuracy of the results has been tested by comparing them with available experimental and theoretical values (ASI-CAST project is acknowledged).     

Cyclodextrin derivatives in the GC separation of racemic mixtures of volatile compounds: Part IV

This paper reports the chromatographic performance of columns coated with 2,3,6-trimethyl-α-, β-, and γ-cyclodextrins (2,3,6-TriMe-α,- β-, and γ-CD) and their derivatives 2,6-dimethyl-3-trifluoroacetyl-α-, β-, and γ-cyclodextrins (2,6-DiMe-3-TFA-α-, β-, and γ-CD), all six diluted in polysiloxane, for the separation of the enantiomers of volatile compounds. The influence of column length and film thickness on separation is reported. Phenomena related to reproducibility and consistency, over a period of time, of columns prepared with these CD derivatives are also discussed, and a possible solution to some drawbacks reported here is proposed.     

Inexact spectral projected gradient methods on convex sets

A new method is introduced for large-scale convex constrainedoptimization. The general model algorithm involves, at eachiteration, the approximate minimization of a convex quadraticon the feasible set of the original problem and global convergenceis obtained by means of nonmonotone line searches. A specificalgorithm, the Inexact Spectral Projected Gradient method (ISPG),is implemented using inexact projections computed by Dykstra'salternating projection method and generates interior iterates.The ISPG method is a generalization of the Spectral ProjectedGradient method (SPG), but can be used when projections aredifficult to compute. Numerical results for constrained least-squaresrectangular matrix problems are presented.