Related papers: A stratified polyhedral homotopy method for sampli…
To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spaltenstein solved this problem for chain complexes of R-modules by truncating further and further to the left, resolving…
We present a covariant model of a spherically symmetric black hole with corrections motivated by loop quantum gravity. The effective modifications, parametrized by a positive constant $\lambda$, are implemented through a canonical…
The uniqueness and rigidity of black holes remain central themes in gravitational research. In this work, we investigate the construction of all extremal black hole solutions to the Einstein equation for a given near-horizon geometry,…
The main aim of this work is to apply the matrix approach of ortho\-gonal polynomials associated with infinite Hermitian definite positive matrices in relation with an important question regarding the location of zeros of Sobolev orthogonal…
In this work we address a way to capture scalar field solutions on static spacetimes by using BPS formalism and relaxing the general covariance condition. We focus on configurations where the background geometry describes topological black…
In this paper, we are concerned with the problem of counting the multiplicities of a zero-dimensional regular set's zeros. We generalize the squarefree decomposition of univariate polynomials to the so-called pseudo squarefree decomposition…
This paper presents a new algorithm for the convex hull problem, which is based on a reduction to a combinatorial decision problem POLYTOPE-COMPLETENESS-COMBINATORIAL, which in turn can be solved by a simplicial homology computation. Like…
In this paper, we compute the BP-cohomology of complex projective Stiefel manifolds. The method involves the homotopy fixed point spectral sequence, and works for complex oriented cohomology theories. We also use these calculations and…
In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point. To illustrate our method, we consider the Tricomi-Carlitz polynomials…
We implement a real polyhedral homotopy method using three functions. The first function provides a certificate that our real polyhedral homotopy is applicable to a given system; the second function generates binomial systems for a start…
This paper is devoted to the study of the $m$-point homogeneity property for the vertex sets of polytopes in Euclidean spaces. In particular, we present the classifications of $2$-point and $3$-point homogeneous polyhedra in $\mathbb{R}^3$.
We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensaetze) from real algebraic geometry can be generalized to noncommutative $*$-algebras. A…
In this paper we introduce universal asymptotic unfolding normal forms for nonlinear singular systems. Next, we propose an approach to find the parameters of a parametric singular system that they play the role of universal unfolding…
We construct an effective algorithmic method to compute the homological monodromy of a complex polynomial which is tame. As an application we show the existence of conjugated polynomials in a number field which are not topologically…
In recent developments, a general approach for solving Riemann--Hilbert problems numerically has been developed. We review this numerical framework, and apply it to the calculation of orthogonal polynomials on the real line. Combining this…
In this paper we present a new approach to the study of asymptotically flat static metrics arising in general relativity. In the case where the static potential is bounded, we introduce new quantities which are proven to be monotone along…
Geometric involutive bases for polynomial systems of equations have their origin in the prolongation and projection methods of the geometers Cartan and Kuranishi for systems of PDE. They are useful for numerical ideal membership testing and…
Studied here is the effect of the presence of symmetry groups in a system of algebraic equations on the numerical resolution with fixed-point algorithms. It is proved that the symmetries imply two important properties of the system: the…
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This…
We present a symbolic-numeric method to refine an approximate isolated singular solution $\hat{\mathbf{x}}=(\hat{x}_{1}, ..., \hat{x}_{n})$ of a polynomial system $F=\{f_1, ..., f_n\}$ when the Jacobian matrix of $F$ evaluated at…