Air transparent soundproof window

A soundproof window or wall which is transparent to airflow is presented. The design is based on two wave theories of diffraction and acoustic metamaterials. It consists of a three-dimensional array of strong diffraction-type resonators with many holes centered at each individual resonator. The acoustic performance levels of two soundproof windows with air holes of $20mm$ and $50mm$ diameters were measured. Sound waves of 80dB in the frequency range of $400 - 5,000Hz$ were applied to the windows. It was observed that the sound level was reduced by about $30 - 35$dB in the above frequency range with the $20mm$ window and by about $20 - 35$dB in the frequency range of $700 - 2,200Hz$ with the $50mm$ window. It is an extraordinary acoustic anti-transmission. The geometric factors which produced the effective negative modulus were obtained.Comment: 4 pages, 6 figures, 1 tabl

Quartically hyponormal weighted shifts need not be 3-hyponormal

We give the first example of a quartically hyponormal unilateral weighted shift which is not 3-hyponormal