Reconstructing and designing media with continuously-varying refractive index fields remains a challenging problem in computer graphics. A core difficulty trying to tackle this inverse is that light travels inside such along curves, rather than straight lines. Existing techniques for make strong assumptions on the shape of ray medium, thus limit themselves where deflection relatively small. Mor...

We extend the concept of Lifshits–Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of (admissible) operators that are similar to self-adjoint operators. An operator H is called admissible if: (i) there is a bounded operator V with a bounded inverse such that H = V −1 HV for some self-adjoint operator H; (ii) the operators H and H are resolvent ...

We obtain bounds on the complex eigenvalues of nonself-adjoint Schrödinger operators with complex potentials, and also on the complex resonances of self-adjoint Schrödinger operators. Our bounds are compared with numerical results, and are seen to provide useful information.

It is known that the so-called monadic decomposition, applied to adjunction connecting category of bialgebras vector spaces via tensor and primitive functors , returns usual between (restricted) Lie algebras . Moreover, in this framework, notions augmented monad combinatorial rank play a central role. In order set these results into wider context, we are led substitute decomposition by what cal...

In this work we consider the problem on group classification and conservation laws of general first order evolution equations. We obtain subclasses these equations which are quasi-self-adjoint self-adjoint. By using recent Ibragimov's Theorem laws, establish admiting self-adjoint illustrate our results applying them to inviscid Burgers' equation. particular an infinite number new symmetries fou...

We use C *-algebra theory to provide a new method of decomposing the essential spectra of self-adjoint and non-self-adjoint Schrödinger operators in one or more space dimensions.