On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

Non-display uses of digital works: Google Books and beyond

With the advent of mass digitization projects, such as the Google Book Search, a peculiar shift has occurred in the way that copyright works are dealt with. Contrary to what has so far been the case, works are turned into machine-readable data to be automatically processed for various purposes without the expression of works being displayed to the public. In the Google Book Settlement Agreement, this new kind of usage is referred to as ‘non-display uses’ of digital works. The legitimacy of these uses has not yet been tested by Courts and does not comfortably fit in the current copyright doctrine, plainly because the works are not used as works but as something else, namely as data. Since non-display uses may prove to be a very lucrative market in the near future, with the potential to affect the way people use copyright works, we examine non-display uses under the prism of copyright principles to determine the boundaries of their legitimacy. Through this examination, we provide a categorization of the activities carried out under the heading of ‘non-display uses’, we examine their lawfulness under the current copyright doctrine and approach the phenomenon from the spectrum of data protection law that could apply, by analogy, to the use of copyright works as processable data.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.