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We study Hilbert-Kunz multiplicity of the powers of an ideal and establish existence of the second coefficient at the full level of generality, thus extending a recent result of Trivedi. We describe the second coefficient as the limit of the Hilbert coefficients of Frobenius powers and show that it is additive in short exact sequences and satisfies a Northcott-type inequality. [ABSTRACT FROM AUTHOR]

A method for calculating the strength and diffraction parameters, [uppercase_phi_synonym] and Λ is described. Floquet's theorem is shown to be of use in the calculation of Λ for a range-independent sound-speed profile. The sensitivity of Λ and [uppercase_phi_synonym] to changes in the sound-speed profile and the buoyancy-frequency profile is investigated. It is shown that rays with large intensity tend to have small [uppercase_phi_synonym] and small Λ except very near caustics. [Work supported by ONR Code 480.] [ABSTRACT FROM AUTHOR]

Most of what is known about the nature of acoustic emission sources has been learned through the use of piezoelectric transducers coupled to rectangular parallelepiped or plate-type specimens. Unfortunately, the output of the piezoelectric transducer is not a true picture of the source signal; rather, it is the acoustic emission signal modified by the responses of the specimen, the specimen-transducer interface, and the transducer. As a first step in determining what acoustic emission looks like, this paper presents a closed-form normal mode solution for the forced vibrational response of a rectangular parallelepiped with stress-free boundaries. Knowing the specimen response will allow the calibration of piezoelectric transducers for all three wave types-dilational, transverse, and surface waves-and this, in turn, will allow the characterization of acoustic emission sources. [ABSTRACT FROM AUTHOR]

The need for improved isolation for operators of off-road vehicles is discussed. Referring specifically to agricultural vehicles, a review is made of some of the approaches taken in North America and Europe to improve seat suspension systems. Data comparing the performance of active and passive systems is presented. The presentation will be supplemented with slides and film strips. [ABSTRACT FROM AUTHOR]

An approach to prevent noises of large induction motors which are subjected to various forms of vibration caused by electromagnetic exciting forces is presented. From the results obtained in experimental investigations for many actual large motors, it has become clear that all the components of the noise and vibration paths from exciting point to radiational sound field must be taken into consideration for avoiding typical peak noise and vibration. A substructural system analysis is adopted to comprehend the vibrational behavior of all components by using FFT (fast Fourier transform) analysis and the transfer function method. The combined system simulation is done in a digital computer by using modal parameters to estimate the frequency response of the total structure. It means that the contributions of each component to the total noise and vibration are predicted without actual motors. Now, through this investigation, it is considered possible to predict quantitatively the effects of each component al least on vibration. [ABSTRACT FROM AUTHOR]

The propagator matrix formalism is a convenient method for treating horizontally stratified media [F. Gilbert and G. E. Backus, Geophysics 31, 326 (1966)]. Until now, however, it apparently has not been applied to periodic media. This paper shows how the propagator formalism can be used in conjunction with Sylvester's theorem to obtain an extract solution for the propagation of waves in a periodically stratified layer of arbitrary thickness. Explicit expressions are derived for the simple case of a periodically layered fluid. These expressions are used to investigate several interesting limiting cases. Application of the method to more complicated cases is discussed. [ABSTRACT FROM AUTHOR]