Related papers: An introduction to filtered and synthetic spectra
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
Expanded lecture notes. Preliminary version, comments are welcome.
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
Beginning with a historical account of the spectral classification, its refinement through additional criteria is presented. The line strengths and ratios used in two dimensional classifications of each spectral class are described. A…
We extend Homotopy Type Theory with a novel modality that is simultaneously a monad and a comonad. Because this modality induces a non-trivial endomap on every type, it requires a more intricate judgemental structure than previous modal…
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Optical spectroscopy is an important and widely used technique, for instance, to characterize new materials and to identify unknown compounds. Spectra are typically reported as a function of the wavelength of light, yet the information…
The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.
The concept of unique normal form is formulated in terms of a spectral sequence. As an illustration of this technique some results of Baider and Churchill concerning the normal form of the anharmonic oscillator are reproduced. The aim of…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit…
In this paper, we develop a structure theory for generalized spectral sequences, which are derived from chain complexes that are filtered over arbitrary partially ordered sets. Also, a more general construction method reminiscent of exact…
In these introductory notes I give a brief overview on some theoretical aspects of light baryon spectroscopy. The first part contains a discussion of the symmetries of the baryon spectrum, the construction of flavor wave functions and some…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the…