Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions

We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also make some relevant conjectures for the admissible constant curvatures in G(m, n) and give some explicit expressions, in particular, for G(2, 4) and G(2, 5).Comment: 14 page

Topology of modified helical gears and Tooth Contact Analysis (TCA) program

The contents of this report covers: (1) development of optimal geometries for crowned helical gears; (2) a method for their generation; (3) tooth contact analysis (TCA) computer programs for the analysis of meshing and bearing contact of the crowned helical gears; and (4) modelling and simulation of gear shaft deflection. The developed method for synthesis was used to determine the optimal geometry for a crowned helical pinion surface and was directed to localize the bearing contact and guarantee favorable shape and a low level of transmission errors. Two new methods for generation of the crowned helical pinion surface are proposed. One is based on the application of a tool with a surface of revolution that slightly deviates from a regular cone surface. The tool can be used as a grinding wheel or as a shaver. The other is based on a crowning pinion tooth surface with predesigned transmission errors. The pinion tooth surface can be generated by a computer-controlled automatic grinding machine. The TCA program simulates the meshing and bearing contact of the misaligned gears. The transmission errors are also determined. The gear shaft deformation was modelled and investigated. It was found that the deflection of gear shafts has the same effect as gear misalignment

Robust Adaptive Control of a Class of Nonlinear Strict-feedback Discrete-time Systems with Exact Output Tracking

10.1016/j.automatica.2009.07.025Automatica45112537-2545ATCA

Interactions of Tone and Intonation in Whispered Mandarin

A previous study has found that whispered Mandarin, though still allowing listeners to perceive tones to a certain degree, does not carry acoustic cues that are special to whispered tones. That conclusion, however, was based on data from only one speaker. The present study attempted to verify the earlier finding with data from more speakers, with an additional goal to find out if there are acoustic cues to intonation in whispered Mandarin and whether they interact with tonal cues. Twelve Mandarin speakers produced tonal as well as intonational contrasts in both phonated and whispered speech. Acoustic analyses found that whispered questions had longer duration, greater intensity and shallower spectral tilt than statements. However, a perception experiment with 20 native listeners showed a strong bias toward hearing statement in whispers, so that questions were identified well below chance. Thus the acoustic properties in whisper were countering each other as cues to intonation. There was also an interaction of tone and intonation in whispers in that Tone 2 and question help each other while Tone 4 and question hinder each other in their perceptual identification. Overall, therefore, there do not seem to be special perceptual cues to whispered intonation either