Nonlinearity of water

Forward model nonlinearity versus inverse model nonlinearity.

The issue of concern is the impact of forward model nonlinearity on the nonlinearity of the inverse model. The question posed is, "Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity in the inverse solution (estimation of hydraulic conductivity)?" It is shown that the two nonlinearities are separate, and it is not universally true that increa...

Simplified nonlinearity correction of oxygen-15-water regional cerebral blood flow images without blood sampling.

UNLABELLED A noninvasive method, the double-integration method, was developed to estimate regional cerebral blood flow (rCBF) by using 15O-water and PET. It relies on the acquisition of images with a correction of nonlinearity of brain tissue counts and can produce rCBF images on a pixel-by-pixel basis. METHODS Oxygen-15-water PET studies were performed on five normal human volunteers, and co...

Nonlinearity of Matrix Groups

The aim of this short note is to answer a question by Guoliang Yu of whether the group EL3(Z〈x, y〉), where Z〈x, y〉 is the free (non-commutative) ring, has any faithful finite dimensional linear representations over a field. Recall that for every (associative unitary) ring R the group ELn(R) is the subgroup of GLn(R) generated by all n × n-elementary matrices xij(r) = Id + reij (r ∈ R, 1 ≤ i 6= ...

Four Measures of Nonlinearity

Cryptographic applications, such as hashing, block ciphers and stream ciphers, make use of functions which are simple by some criteria (such as circuit implementations), yet hard to invert almost everywhere. A necessary condition for the latter property is to be “sufficiently distant” from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that f...

Nonlinearity pdf