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Conditions for separately subharmonic functions to be subharmonic
Potential Analysis, 1993Let \(\Omega\) be an open set in \(\mathbb{R}^ m \times \mathbb{R}^ n\). A function \(u\) is separately subharmonic on \(\Omega\) if \(u(x,\cdot)\) is subharmonic on the \(x\)-section of \(\Omega\), and \(u(\cdot,y)\) on the \(y\)-section, for all \((x,y) \in\Omega\).
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Nondestructive subharmonic imaging
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2002Ultrasound contrast agent microbubbles are intravascular agents that can be used to estimate blood perfusion. Blood perfusion may be estimated by destroying the bubbles in a vascular bed and observing the refresh of contrast agents back into the vascular bed. Contrast agents can be readily destroyed by traditional imaging techniques.
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AN ESTIMATE FOR THE SUBHARMONIC DIFFERENCE OF SUBHARMONIC FUNCTIONS. I
Mathematics of the USSR-Sbornik, 1977Let , , and be subharmonic functions in the half-plane , and suppose that and are majorized by a positive function of the form , where and .An inequality for the subharmonic difference is obtained in terms of the function , , , which then gives an estimate for the difference from above.
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