相关论文: Continuation Methods for Computing Z-/H-eigenpairs…

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…

We study the foundational properties of persistent homotopy groups and develop elementary computational methods for their analysis. Our main theorems are persistent analogues of the Van Kampen, excision, suspension, and Hurewicz theorems.…

A lot of good properties of etale cohomology only hold for torsion coefficients. We use "enlargement of categories" as developed in http://arxiv.org/abs/math.CT/0408177 to define a cohomology theory that inherits the important properties of…

In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. Also the class of Pascal finite polynomial automorphisms was introduced. Pascal finite polynomial maps constitute a generalization of…

We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new…

In this paper, we provide a system-theoretic treatment of certain continuous-time homogeneous polynomial dynamical systems (HPDS) via tensor algebra. In particular, if a system of homogeneous polynomial differential equations can be…

Given compact Lie groups H\subset G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K…

First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…

We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the…

This work is concerned with the computation of $\ell^p$-eigenvalues and eigenvectors of square tensors with $d$ modes. In the first part we propose two possible shifted variants of the popular (higher-order) power method %for the…

For each positive integer Q there exists a path connected metric compactum X such that the Qth-homotopy group of X is compactly generated but not a topological group (with the quotient topology).

We prove an extension of the homology version of the Hofer-Zehnder conjecture proved by Shelukhin to the weighted projective spaces which are symplectic orbifolds. In particular, we prove that if the number of fixed points counted with…

In this paper, we consider higher order paired symmetric tensors and strongly paired symmetric tensors. Elasticity tensors and higher order elasticity tensors in solid mechanics are strongly paired symmetric tensors. A (strongly) paired…

Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…

Noncommutative topological entropy estimates are obtained for polynomial gauge invariant endomorphisms of Cuntz algebras, generalising known results for the canonical shift endomorphisms. Exact values for the entropy are computed for a…

While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a…

Using standard calculus, explicit formulas for one-, two- and three-dimensional homotopy operators are presented. A derivation of the one-dimensional homotopy operator is given. A similar methodology can be used to derive the…

We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…

In this article, we develop and analyze a homotopy continuation method, referred to as HONES , for solving the sequential generalized projections in Online Newton Step, as well as the generalized problem known as sequential standard…