Related papers: Realizing arbitrarily large spectra of $\mathfrak{…
This paper discusses some of the challenges of spectro-polarimetric observations with a large aperture solar telescope such as the ATST or the EST. The observer needs to reach a compromise among spatial and spectral resolution, time…
We present a simple but effective method to extract the reflectivity spectra from the interference signals with a large NA white light interferometry. Numerical simulations and experiments have demonstrated the effectiveness of our method.…
As telescopes get larger, the size of a seeing-limited spectrograph for a given resolving power becomes larger also, and for ELTs the size will be so great that high resolution instruments of simple design will be infeasible. Solutions…
We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of products of four automorphic forms. Using a combination of…
In this paper we study the absolute convergence of the spectral side of the Arthur trace formula. We reduce the problem of the absolute convergence to a problem about local components of automorphic representations. The latter problem can…
We prove new explicit inapproximability results for the Vertex Cover Problem on the Power Law Graphs and some functional generalizations of that class of graphs. Our results depend on special bounded degree amplifier constructions for those…
A list $\Lambda =\{\lambda _{1},\ldots ,\lambda _{n}\}$ of complex numbers (repeats allowed) is said to be \textit{realizable} if it is the spectrum of an entrywise nonnegative matrix $A$. $\Lambda $ is \textit{diagonalizably realizable} if…
In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…
We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning the representation of eigenvectors and the asymptotic…
We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a…
We use atomic spectra to extend pure Coulomb's law tests to larger masses. We interpret these results in terms of constraints for hidden sector photons. With existing data the bounds for hidden photons are not improved. However we find that…
Context: The technique of disentangling has been applied to numerous high-precision studies of spectroscopic binaries and multiple stars. Although, its possibilities have not yet been fully understood and exploited. Aims: Theoretical…
We give a proof of a phenomenon conjectured in our former article: "Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening". We also start an abstract discussion of the notion of limits of…
The determination of photospheric abundances in late-type stars from spectroscopic observations is a well-established field, built on solid theoretical foundations. Improving those foundations to refine the accuracy of the inferred…
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general…
We introduce multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic…
We consider the topological relation behind the spectral behavior of a linear operator that arises in the stability problem of traveling waves on a large bounded domain. When the domain size tends to infinity, the absolute and asymptotic…
Spectral representations have been shown to provide an efficient way to represent the poorly understood high-density portion of the neutron-star equation of state. This paper shows how the efficiency and accuracy of those representations…
A new mechanism of Bragg reflection is identified, one that, remarkably, occurs in a uniform medium and relies on resonant tuning of the medium's parameters. Due to uniformity, reflection ensues over a broad wavelength range, much like a…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…