On the tensor operators in parallelizable spaces

The tensor-operators over parallelizable spaces are defined. Their Hermitian conjugation is defined by introducing an inner product based on the tensor-integral Some properties of the ordinary operators are generalized for the tensor-operators     

Dynamics and Correlates of Microscopic Changes in Affect

How are momentary microscopic assessments of behavioral dynamics related to traditional macroscopic, static measures? The present study used the computerized “mouse paradigm” to assess near-instantaneous changes in affect over a short time. Dynamic indices were computed from approximately 1400 measurements from the last 2.5 minutes of a 3-minute assessment. Subjects monitored and reported emotional states by moving a cursor along a dimension from “Sadder” to “Happier.” They also completed self-report measures: Scales 2 (Depression) and 9 (Mania) of the MMPI-2, the Positive and Negative Affect Scale, and the Wisconsin scales of Physical Anhedonia and Hypomanic traits. The instantaneous data yielded a summary measure of mean affect, as well as indices of variability. Complexity indices were derived and examined. Mean affect ratings correlated in expected directions with the paper and pencil measures. There was evidence for low-dimensional chaos in short-term affect dynamics. As hypothesized, greater complexity was associated with Pleasant Affect and Hypomania but was negatively correlated with Anhedonia.     

Non-leptonic hadron decays and field algebra (I). Parity violating amplitudes

This paper describes the application to parity-violating non-leptonic decays of a model of weak interactions, based on the algebra of fields definition of the hadron currents that participate in weak interactions. Symmetry breaking effects are included, octet dominance is built in explicitly and a careful treatment is given of the diagonalization procedure needed to identify the physical 0⁻ and 1^± fields. Agreement with experiment comparable to that of K^∗ pole and current algebra models is achieved.     

Methods for the structural investigation of xanthones: Part II. Location of hydroxyl groups by ultraviolet and visible spectroscopy1

Ultraviolet spectral shifts in presence of certain additives may be used to determine the hydroxylation pattern of xanthones. Thus, 3-hydroxyxanthones are characterized by an intense band around 355 nm which appears in presence of sodium hydroxide, o- and p-Dihydroxyxanthones decompose in presence of this reagent, the reaction rate depending on the position of the substituents. While the spectra of 1-and 2-hydroxyxanthones do not suffer modification in presence of sodium acetate, 3- and 4-hydroxy groups produce typical shifts which are dependent on the presence of additional oxygen functions. The spectra of 1-hydroxy-, as well as of o-dihydroxyxanthones, are affected by the addition of aluminum chloride. 1- and 4-Hydroxy groups with unsubstituted p-positions may be detected and distinguished through the visible spectrum (350–750 nm) of the reaction product of the xanthone with 2,6-dichlorobenzoquinone chloroimide (Gibbs test). Relatively acidic hydroxyls give rise to two maxima in this region. Two maxima, even if of different relative intensity, are also obtained with o- and p-dihydroxy-, as well as with o- and p-hydroxyallylxanthones.     

Rotational spectra of vibrationally excited CCH and CCD

The millimeter-wave rotational spectra of the lowest bending and stretching vibrational levels of CCH and CCD were observed in a low pressure discharge through acetylene and helium. The rotational, centrifugal distortion, and fine structure constants were determined for the (02(0)0) and (02(2)0) bending states, the (100) and (001) stretching levels, and the (011) combination level of CCH. The same pure bending and stretching levels, and the (110) combination level were observed in CCD. Apparent anomalies in the spectroscopic constants in the bending states were shown to be due to l-type resonances. Hyperfine constants, which in CCH are sensitive to the degree of admixture of the A 2Pi excited electronic state, were determined in the excited vibrational levels of both isotopic species. Theoretical Fermi contact and dipole-dipole hyperfine constants calculated by Peric et al. [J. Mol. Spectrosc. 150, 70 (1991)] were found to be in excellent agreement with the measured constants. In CCD, new rotational lines tentatively assigned to the (100) level largely on the basis of the observed hyperfine structure support the assignment of the C-H stretching fundamental (nu1) by Stephens et al. [J. Mol. Struct. 190, 41 (1988)]. Rotational lines in the excited vibrational levels of CCH are fairly intense in our discharge source because the vibrational excitation temperatures of the bending vibrational levels and the (110) and (011) combination levels are only about 100 K higher than the gas kinetic temperature, unlike the higher frequency stretching vibrations, where the excitation temperatures are five to ten times higher.     

Nonlinear dynamic behavior of a microbeam array subject to parametric actuation at low,medium and large DC-voltages

The dynamic response of parametrically excited microbeam arrays is governed by nonlinear effects which directly influence their performance. To date, most widely used theoretical approaches, although opposite extremes with respect to complexity, are nonlinear lumped-mass and finite-element models. While a lumped-mass approach is useful for a qualitative understanding of the system response it does not resolve the spatio-temporal interaction of the individual elements in the array. Finite-element simulations, on the other hand, are adequate for static analysis, but inadequate for dynamic simulations. A third approach is that of a reduced-order modeling which has gained significant attention for single-element micro-electromechanical systems (MEMS), yet leaves an open amount of fundamental questions when applied to MEMS arrays. In this work, we employ a nonlinear continuum-based model to investigate the dynamic behavior of an array of N nonlinearly coupled microbeams. Investigations focus on the array’s behavior in regions of its internal one-to-one, parametric, and several internal three-to-one and combination resonances, which correspond to low, medium and large DC-voltage inputs, respectively. The nonlinear equations of motion for a two-element system are solved using the asymptotic multiple-scales method for the weakly nonlinear system in the afore mentioned resonance regions, respectively. Analytically obtained results of a two-element system are verified numerically and complemented by a numerical analysis of a three-beam array. The dynamic behavior of the two- and three-beam systems reveal several in- and out-of-phase co-existing periodic and aperiodic solutions. Stability analysis of such co-existing solutions enables construction of a detailed bifurcation structure. This study of small-size microbeam arrays serves for design purposes and the understanding of nonlinear nearest-neighbor interactions of medium- and large-size arrays. Furthermore, the results of this present work motivate future experimental work and can serve as a guideline to investigate the feasibility of new MEMS array applications.