相关论文: Realizing arbitrarily large spectra of $\mathfrak{…
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T\colon \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we…
We study the decision version of tensor spectral norm from the viewpoint of real algebraic complexity. For a rationally specified tensor, the tensor spectral threshold problem asks whether its spectral norm exceeds a prescribed rational…
We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to…
A method for constructing optical potentials with an arbitrary distribution of gain and loss and completely real spectrum is presented. For each arbitrary distribution of gain and loss, several classes of refractive-index profiles with…
We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things we investigate consequences of…
A photonic spectrograph can be much smaller than a conventional spectrograph with the same resolving power. Individual devices can be integrated with optical fibres to improve the multiplex gain in astronomical spectroscopy. Although…
We develop the requirements and potential of spectropolarimetry as applied to understanding the physics of massive stars during the immediate, intermediate-term and long-term future.
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
We develop a matrix bordering technique that can be applied to an irreducible spectrally arbitrary sign pattern to construct a higher order spectrally arbitrary sign pattern. This technique generalizes a recently developed triangle…
In this paper, we study the spectrality of infinite convolutions generated by infinitely many admissible pairs which may not be compactly supported, where the spectrality means the corresponding square integrable function space admits a…
In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. As an example, we demonstrate that a quadratic…
Let G be an even orthogonal or unitary group over a number field. Based on the same observation used in arXiv:1705.10106, we prove the Arthur's multiplicity formula for the generic part of the automorphic discrete spectrum of G by using the…
We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…
We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra $\mathbb{A}^n$. In the case $n=2$ we provide a detailed and, in most cases, complete description of these spectra.
As the multiplexing power of spectroscopic instruments increases, so does the need for automated analysis. In practice, the bottleneck for speed is the calculation of model spectra to evaluate the likelihood of candidate parameters. This…
A matrix pattern is often either a sign pattern with entries in {0,+,-} or, more simply, a nonzero pattern with entries in {0,*}. A matrix pattern A is spectrally arbitrary if for any choice of a real matrix spectrum, there is a real matrix…
A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large…
This is the third article in a series of three dealing with the exploitation of speckle for imaging purposes. In complex media, a fundamental limit is the multiple scattering phenomenon that completely blurs the imaging process in depth.…
We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…