Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Square

An alternating sign matrix, or ASM, is a $(0, \pm 1)$-matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an $n\times n\times n$ hypermatrix $A=[a_{ijk}]$ is an {\em alternating sign hypermatrix}, or ASHM, if each of its planes, obtained by fixing one of the three indices, is an ASM. Several results concerning ASHMs are shown, such as finding the maximum number of nonzeros of an $n\times n\times n$ ASHM, and properties related to Latin squares. Moreover, we investigate completion problems, in which one asks if a subhypermatrix can be completed (extended) into an ASHM. We show several theorems of this type.Comment: 39 page

Acoustical evaluation of the NASA Lewis 9 by 15 foot low speed wind tunnel

The test section of the NASA Lewis 9- by 15-Foot Low Speed Wind Tunnel was acoustically treated to allow the measurement of acoustic sources located within the tunnel test section under simulated free field conditions. The treatment was designed for high sound absorption at frequencies above 250 Hz and to withstand tunnel airflow velocities up to 0.2 Mach. Evaluation tests with no tunnel airflow were conducted in the test section to assess the performance of the installed treatment. This performance would not be significantly affected by low speed airflow. Time delay spectrometry tests showed that interference ripples in the incident signal resulting from reflections occurring within the test section average from 1.7 dB to 3.2 dB wide over a 500 to 5150 Hz frequency range. Late reflections, from upstream and downstream of the test section, were found to be insignificant at the microphone measuring points. For acoustic sources with low directivity characteristics, decay with distance measurements in the test section showed that incident free field behavior can be measured on average with an accuracy of +/- 1.5 dB or better at source frequencies from 400 Hz to 10 kHz. The free field variations are typically much smaller with an omnidirectional source

Comparison between design and installed acoustic characteristics of NASA Lewis 9- by 15-foot low-speed wind tunnel acoustic treatment

The test section of the NASA Lewis 9- by 15-Foot Low-Speed Wind Tunnel was acoustically treated to allow the measurement of sound under simulated free-field conditions. The treatment was designed for high sound absorption at frequencies above 250 Hz and for withstanding the environmental conditions in the test section. In order to achieve the design requirements, a fibrous, bulk-absorber material was packed into removable panel sections. Each section was divided into two equal-depth layers packed with material to different bulk densities. The lower density was next to the facing of the treatment. The facing consisted of a perforated plate and screening material layered together. Sample tests for normal-incidence acoustic absorption were also conducted in an impedance tube to provide data to aid in the treatment design. Tests with no airflow, involving the measurement of the absorptive properties of the treatment installed in the 9- by 15-foot wind tunnel test section, combined the use of time-delay spectrometry with a previously established free-field measurement method. This new application of time-delay spectrometry enabled these free-field measurements to be made in nonanechoic conditions. The results showed that the installed acoustic treatment had absorption coefficients greater than 0.95 over the frequency range 250 Hz to 4 kHz. The measurements in the wind tunnel were in good agreement with both the analytical prediction and the impedance tube test data