H‐matrices play an important role in solving linear systems and in many other fields. General conditions for the class of nonsingular H‐matrices are not always easy to check in practice. Therefore, we give some more practical conditions concerning some subclasses of nonsingular H‐matrices.

Resolution of high intensity focused ultrasound (HIFU) focusing is limited by the wave diffraction. We have developed a spherical cavity transducer with two open ends to improve the focusing precision without sacrificing the acoustic intensity (App Phys Lett 2013; 102: 204102). This work aims to theoretically and experimentally investigate the frequency dependence of the acoustic field generated from the spherical cavity transducer with two open ends. The device emits high intensity ultrasound at the frequency ranging from 420 to 470 kHz, and the acoustic field is measured by a fiber optic probe hydrophone. The measured results shows that the spherical cavity transducer provides high acoustic intensity for HIFU treatment only in its resonant modes, and a series of resonant frequencies can be choosen. Furthermore, a finite element model is developed to discuss the frequency dependence of the acoustic field. The numerical simulations coincide well with the measured results.

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