We consider two singular limits: a fast reaction limit with non-monotone nonlinearity and regularization of the forward-backward diffusion equation. derive pointwise identities satisfied by Young measure generated these problems. As result, we obtain an explicit formula for even without non-degeneracy assumption used in previous works. The main new idea is application Radon–Nikodym theorem to d...

ion is not needed. Inverse problems 531 Theorem 6.13. Two Gaussian measures μi = N (mi, Ci), i = 1, 2, on a Hilbert space H are either singular or equivalent. They are equivalent if and only if the following three conditions hold: (i) Im(C 1 ) = Im(C 1/2 2 ) := E, (ii) m1 −m2 ∈ E, (iii) the operator T := ( C−1/2 1 C 1/2 2 )( C−1/2 1 C 1/2 2 )∗ − I is Hilbert–Schmidt in E. In particular, choosin...

For Machine Learning (ML) classification problem, where a vector of x–observations (values of attributes) is mapped to a single y value (class label), a generalized Radon– Nikodym type of solution is proposed. Quantum–mechanics –like probability states ψ2(x) are considered and “Cluster Centers”, corresponding to the extremums of < yψ2(x) > / < ψ2(x) >, are found from generalized eigenvalues pro...

Northamptonshire is classified as a radon affected area, with greater than 1 per cent of domestic dwellings being above the UK Action Level of 200Bq m–3. Workplace radon is also a health risk in Northamptonshire, with a significant number of premises being predicted to be above this Action Level (400Bq m–3). After an extensive survey in National Health Service premises, using track etch detecto...