We study the general problem of behaviour continuum function in presence non-supercompact strongly compact cardinals. begin by showing that it is possible to force violations GCH at an arbitrary cardinal using only strong compactness as our initial assumption. This result due third author. then investigate realising Easton functions and above least measurable limit supercompact cardinals starti...

transmittance and reflectance, the imaginary part can be determined from transmittance data alone. It is possible to use Kramers-Kronig analysis to calculate the real part if the imaginary part is known over a sufficiently broad range. We show that the delta calculated from reflection and transmission data without taking into account roughness may underestimate the real part of the refractive i...

We consider single particle Schrodinger operators with a gap in the energy spectrum. We construct a countable set of exponentially decaying functions, which form a complete, orthonormal basis set for the states below the spectral gap. Each such function is localized near a closed surface. Estimates on the exponential decay rate and a discussion of the geometry of these surfaces is included.

We consider the small eld asymptotics of the ladder lifetime for a single ladder model. Using the convergent perturbation series, we prove that the behavior of the lifetime computed by means of the Fermi Golden Rule is proportional to the correct one with the factor ? 3 2. The relation with usual adiabatic problems is brieey discussed.

We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions that are Wannier-like one direction and Bloch-like other. focus on active bands as given by continuum model proposed Bistritzer MacDonald, [Proc. Natl. Acad. Sci. 108, 12233 (2011)] discuss properties of corresponding functions. then employ study fillings ±3 electrons per m...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.