An analogue of Ryser's Theorem for partial Sudoku squares

In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition could be reformulated in terms of Hall's Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as saying that any partial latin rectangle $R$ can be completed if and only if $R$ satisfies Hall's Condition for partial latin squares. We define Hall's Condition for partial Sudoku squares and show that Hall's Condition for partial Sudoku squares gives a criterion for the completion of partial Sudoku rectangles that is both necessary and sufficient. In the particular case where $n=pq$, $p|r$, $q|s$, the result is especially simple, as we show that any $r \times s$ partial $(p,q)$-Sudoku rectangle can be completed (no further condition being necessary).Comment: 19 pages, 10 figure

Noise characteristics of the O-1 airplane and some approaches to noise reduction

A brief study of the O-1A airplane to determine possible means for reducing the aircraft aural detection distance was conducted. This effort involved measuring the noise signature of the basic airplane, devising methods to attenuate the noise, and then estimating the effect of several selected modifications on the aural detection distance of the aircraft. A relatively simple modification utilizing a 6.5 ft diameter, six-blade propeller and including a muffler having a volume of 0.725 cu ft is indicated to reduce the aural detection distance of the O-1 aircraft from about 6 miles at an altitude of 1,000 ft and 2 to 3 miles at an altitude of 300 ft to approximately half these values. The flyover noise data suggest that routing the exhaust stacks up and over the wing would provide immediate noise reduction of about 5 dB with an attendant reduction in detection distance. Furthermore, all these studies confirm the work of other investigators that the 1/3 octave band (center frequency=125 cps) is the most critical in reducing aural detection distance

The effect of operations on the ground noise footprints associated with a large multibladed, nonbanging helicopter

In order to expand the data base of helicopter external noise characteristics, a flyover noise measurement program was conducted utilizing the NASA Civil Helicopter Research Aircraft. The remotely operated multiple array acoustics range (ROMAAR) and a 2560-m linear microphone array were utilized for the purpose of documenting the noise characteristics of the test helicopter during flyby and landing operations. By utilizing both ROMAAR concept and the linear array, the data necessary to plot the ground noise footprints and noise radiation patterns were obtained. Examples of the measured noise signature of the test helicopter, the ground noise footprint or contours, and the directivity patterns measured during level flyby and landing operations of a large, multibladed, nonbanging helicopter, the CH-53, are presented