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In this paper we present heterodyne control as a technique for digital feedback control of a high-frequency, narrowband micromechanical oscillator. In this technique, isolated and synchronized hardware downconversion and upconversion components are used in conjunction with digital signal processing (DSP) to control the oscillator. Heterodyne control offers reduced computational effort for the digital control of high-frequency, narrow band system, the reduction of noise outside the pass-band, and the generation of lock-in amplifier signals. We present heterodyne control with design criteria in the context of magnetic resonance force microscopy (MRFM) cantilever control. Finally, we present experimental results of heterodyne control applied to an emulated radio-frequency microcantilever system.

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This study tested three scoring keys for the MTAI—the published empirical key (E); a logical key with three different weights, i.e., + 1, 0, ‐1; and a new logical key with five different scoring weights, one for each of the five responses in MTAI items, i.e., +2, +1, 0, ‐1, ‐2. The latter, termed the pentachotomous‐logical (P‐L), provided scores with slightly higher internal consistency and a frequency distribution which is not so significantly skewed as the others and which provides greater spread among extreme positive and negative scores. Use of the P‐L scoring weights would facilitate the psychological interpretation of the MTAI. However, conclusion that the P‐L scoring key is an improvement must be tempered by the fact that an expected increase in construct validity was not found.

“McKay's Theorem” is the title of a recent article in the Mathematics Teacher (Sberzer 1973). It reports an incident of sudden insight by a student named McKay and the reaction of his teacher, Laurence Sherzer. In brief, Sherzer reports that he nearly snatched defeat from the jaws of victory when he was tempted to say, “No, McKay, that's not how it's done.”