On the generation of side-edge flap noise

A theory is proposed for estimating the noise generated at the side edges of part span trailing edge flaps in terms of pressure fluctuations measured just in-board of the side edge on the upper surface of the flap. Asymptotic formulae are developed in the opposite extremes of Lorentz contracted acoustic wavelength large/small compared with the chord of the flap. Interpolation between these limiting results enables the field shape and its dependence on subsonic forward flight speed to be predicted over the whole frequency range. It is shown that the mean width of the side edge gap between the flap and the undeflected portion of the airfoil has a significant influence on the intensity of the radiated sound. The results indicate that the noise generated at a single side edge of a full scale part span flap can exceed that produced along the whole of the trailing edge of the flap by 3 dB or more.     

Hydrogen shifts in the decomposition of branched chain alkane radical cations

Heat of formation data are consistent with formation of the t-butyl ion when C₃H₇ is eliminated from the molecular ion of 2-methylhexane. The 1–2 hydrogen shift that must accompany this reaction is confirmed via a deuterium isotope effect upon the low energy metastable decomposition.     

Explicit solutions to the reverse order law (AB)+ = B-mrA-lr

Shinozaki and Sibuya have shown that the Moore-Penrose inverse (AB)⁺ can always be expressed as B^-A^- for generalized inverses A^- and B^- of matrices A and B, respectively. In this paper, explicit solutions B^-_mr and A^-_lr to (AB)⁺ = B^-_mrA^-_lr are given. A class of solutions is obtained which is related to an equation of Greville, and expressions for the general solutions are presented.     

Directional correlations of gamma cascades in153Gd

TheEC-decay of¹⁵³Tb to the levels of¹⁵³Gd has been studied in singles and coincidence mode using high resolution x-ray andγ-ray Ge(Li) detectors. The results, in general, are in agreement with the recent findings of Tuurnalaet al. showing a very high density of low-spin states in¹⁵³Gd. The results of theγγ directional correlation experiment using two Ge(Li) detectors together with the I.C.C. data have been used in assigning the spin and parity of 5/2^?, 5/2^?, 3/2^?, 3/2⁺, 5/2⁺, 3/2⁺ and 3/2⁺ to the 41.6, 109.8, 129.1, 212.0, 303.5, 945.6 and 1102.0 keV states respectively. Multipolarity assignments to majority of theγ-transitions have been made from the I.C.C. data obtained through the knowledge of ourγ-ray intensities and the published conversion-electron intensities. From the multipole characters of theγ-transitions, parity assignments have been made to seven states in¹⁵³Gd. Our results have been discussed and compared with that of Tuurnalaet al.     

Local supersymmetry for spinning particles

First and second order forms of the covariant action for a spinning particle are exhibited. The action consistently incorporates the necessary constraints and is invariant under both local supersymmetry and general time parameter transformations, and provides a simple one-dimensional model for the interaction between matter and supergravity. A formulation invariant under general co-ordinate transformations in superspace is also given and shown to be equivalent to the locally supersymmetric one.     

Aggregation of Markov processes: Axiomatization

We give two simple axioms that characterize a simple functional form for aggregation of column stochastic matrices (i.e., Markov processes). Several additional observations are made about such aggregation, including the special case in which the aggregated process is Markovian relative to the original one.     

The two-loop β-function in models with extended rigid supersymmetry

The two-loop propagators and β-function of a general N =2 supersymmetric model comprising N = 2 Yang-Mills coupled to sets of N = 2 hypermultiplets are calculated by N = 1 supergraph techniques. It is shown that all such models are finite at two loops while a subset is also finite at the one-loop level. The calculation thus confirms the finiteness theorems, and shows that they are valid at the two-loop level even if the hypermultiplet is in a complex representation of the gauge group.     

Mechanistic information from deuterium isotope effects on mass spectral processes: The elimination of ketene from acetanilides and the subsequent loss of HNC

Elimination of ketene from the molecular ion of p-chloroacetanilide takes place via a 4-membered transition state, as evidenced by deuterium isotope effects on competing metastable transitions.