Related papers: Synthetic spectra are (usually) cellular
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator…
To any essentially small tensor-triangulated category $\mathcal{K}$ and Thomason subset $Y \subseteq \mathrm{Spc}(\mathcal{K})$ we associate a ringed space $(\mathrm{Spf}(\mathcal{K},Y), \mathcal{O}_{\mathrm{Spf}(\mathcal{K},Y)}),$ called…
Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n <n|A_{alpha}|n><n|A_{alpha'}|n>/(E-E_n) are obtained by harmonic inversion of a cross-correlation signal…
This paper brings together C*-algebras and algebraic topology in terms of viewing a C*-algebraic invariant in terms of a topological spectrum. E-theory, E(A,B), is a bivariant functor in the sense that is a cohomology functor in the first…
Earth observing satellites carrying multi-spectral sensors are widely used to monitor the physical and biological states of the atmosphere, land, and oceans. These satellites have different vantage points above the earth and different…
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…
The power spectrum formula of the synchrotron radiation generated by the electron and positron moving along the concentric circles at the opposite angular velocities in homogenous magnetic field is derived in the Schwinger version of…
Motivated by the study of persistence modules over the real line, we investigate the category of linear representations of a totally ordered set. We show that this category is locally coherent and we classify the indecomposable injective…
Let R be an E_2 ring spectrum with zero odd dimensional homotopy groups. Every map of ring spectra MU to R is represented by a map of E_2 ring spectra. If 2 is invertible in pi_0(R), then every map of ring spectra MSO to R is represented by…
Inspired by Stewart Priddy's cellular model for the $p$-local Brown-Peterson spectrum $BP$, we give a construction of a $p$-local $E_\infty$ ring spectrum $R$ which is a close approximation to $BP$. Indeed we can show that if $BP$ admits an…
A parametrized spectrum E is a family of spectra E_x continuously parametrized by the points x of a topological space X. We take the point of view that a parametrized spectrum is a bundle-theoretic geometric object. When R is a ring…
The advancements in stellar spectroscopy data acquisition have made it necessary to accomplish similar improvements in efficient data analysis techniques. Current automated methods for analyzing spectra are either (a) data-driven, which…
We give a simple geometric characterization of isospectral orbifolds covered by spheres, complex projective spaces and the quaternion projective line having cyclic fundamental group. The differential operators considered are…
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $\gamma$.…
The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using…
In this survey paper on commutative ring spectra we present some basic features of commutative ring spectra and discuss model category structures. As a first interesting class of examples of such ring spectra we focus on (commutative)…
The object of study in this paper is the on-shell scattering matrix $S(E)$ of the Schr\"odinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of $S(E)$ in the…
The synthesis of antenna arrays in presence of mutual coupling using generalized scattering matrices in terms of characteristic modes is proposed. For the synthesis, the array is built of synthetic elements that are described by their modal…
The emission spectrum of a dipole embedded in a semi-infinite photonic crystal is calculated. For simplicity we study the case in which the dielectric function is sinusoidally modulated only along the direction perpendicular to the boundary…