Related papers: The spectral sequence of a polycomplex
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
The spectral representation is an effecient tool to explore electrical properties of material mixtures. It separates the contributions of geometrical topology and intrinsic properties of the constituents in the system. The aim of this paper…
The Leray spectral sequence of a map $f$ computes the homology of the domain of $f$ from the fibers of $f$. In this expository paper, we relate in full detail the Leray spectral sequence associated to a simplicial map $f$ to the Leray…
We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…
We obtain a description of the spectrum of bidual algebra $A^{**}$ of a uniform algebra $A$. This spectrum turns out to be a quotient space of the hyper-Stonean envelope of the spectrum of $A$.
We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of…
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to some extent, provide insights into the geometry of simplicial…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
A general theory of electronic excitations in aggregates of molecules coupled to intramolecular vibrations and the harmonic environment is developed for simulation of the third-order nonlinear spectroscopy signals. The model is applied in…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
X-ray spectroscopy is a powerful technique for the analysis of the energy distribution of X-rays from astrophysical sources. It allows for the study of the properties, composition, and physical processes taking place at the site of…
Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a…
Starting from the formulation of pseudo-Riemannian generalisation of real spectral triples we develop the data of geometries over finite-dimensional algebras with indefinite metric and their Riemannian parts. We then discuss the Standard…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.
In this paper we get two new classes of regular sequences in the polynomial ring over the field of complex numbers.
A "spectral convex set" is a collection of symmetric matrices whose range of eigenvalues form a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal-Sottile-Sturmfels (2011). We study this class…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
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.