Numerous problems in numerical analysis, including matrix inversion, eigenvalue calculations and polynomial zerofinding, share the following property: The difficulty of solving a given problem is large when the distance from that problem to the nearest "ill-posed" one is small. For example, the closer a matrix is to the set of noninvertible matrices, the larger its condition number with respect...

The security of pairing-based cryptosystems is closely related to the difficulty of the pairing inversion problem. Building on previous works, we provide further contributions on the difficulty of pairing inversion. In particular, we revisit the approach of Kanayama-Okamoto who modified exponentiation inversion and Miller inversion by considering an “auxiliary” pairing. First, by generalizing a...

The concept of flow field velocimetry based on scalar imaging measurements @Phys. Fluids A 4, 2191 ~1992!# is here formulated in terms of an integral minimization implementation, where the velocity field u~x,t! is found by minimizing weighted residuals of the conserved scalar transport equation, along with the continuity condition and a smoothness condition. We apply this technique to direct nu...

Uterine inversion is shortly described as the indentation and depression of the fundic area extending downwards up to the different levels of the birth canal till vaginal opening. Clinical diagnosis of uterine inversion is difficult due to its non-specific symptoms and physical examination. Ultrasonography is the most practical modality for radiological evaluation, but it is inadequate to deter...

Uterine inversion is shortly described as the indentation and depression of the fundic area extending downwards up to the different levels of the birth canal till vaginal opening. Clinical diagnosis of uterine inversion is difficult due to its non-specific symptoms and physical examination. Ultrasonography is the most practical modality for radiological evaluation, but it is inadequate to deter...

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer & Hermand, J. Acoust. Soc. Am. 117, 2937–2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a...