Related papers: Spectral sequences, d\'ecalage, and the Beilinson …
For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the…
In the following, we give an explicit construction of a Laplacian on the Minkowski curve, with energy forms that bear the geometric characteristic of the structure. The spectrum of the Laplacian is obtained by means of spectral decimation.
Through the theory of Lie bi-algebroids and generalized complex structures, one could define a cohomology theory naturally associated to a holomorphic Poisson structure. It is known that it is the hypercohomology of a bi-complex such that…
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)…
One of the basic problems in studying topological structures of deformation spaces for Kleinian groups is to find a criterion to distinguish convergent sequences from divergent sequences. In this paper, we shall give a sufficient condition…
In this work, we develop a spectral theory for hypergraph limits. We prove the convergence of the spectra of adjacency and Laplacian matrices for hypergraph sequences converging in the $1$-cut metric. On the other hand, we give examples of…
Sequences whose terms are equal to the number of functions with specified properties are considered. Properties are based on the notion of derangements in a more general sense. Several sequences which generalize the standard notion of…
Given a sequence of regular finite coverings of complete Riemannian manifolds, we consider the covering solenoid associated with the sequence. We study the leaf-wise Laplacian on the covering solenoid. The main result is that the spectrum…
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…
Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation,…
The theory of generalized locally Toeplitz (GLT) sequences was conceived as an apparatus for computing the spectral distribution of matrices arising from the numerical discretization of differential equations (DEs). The purpose of this…
We study degree spectra of structures with respect to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of its bi-embeddable copies. To facilitate our study we introduce the notions…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph isomorphism. An edge cut is defined by an edge and the…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
The method of spectral disentangling has now created the opportunity for studying the chemical composition in previously inaccessible components of binary and multiple stars. This in turn makes it possible to trace their chemical evolution,…
We show the homological Serre spectral sequence with coefficients in a field is a spectral sequence of coalgebras. We also identify the comultiplication on the $E^2$ page of the spectral sequence as being induced by the usual…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…