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We study the space of stability conditions on the total space of the canonical line bundle over the three dimensional projective space. We construct a family of geometric stability conditions and some subset of the boudary of them, which…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem…
Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving…
The usual definition of the stability region of implicit multistep methods often implies that there are some isolated points of stability within the region of instability of the numerical method. These isolated stable points may appear when…
In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via…
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…
We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin.…
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…
We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial…
A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…
We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore,…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…
We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order…
A polynomial with rational coefficients is said to be pure with respect to a rational prime $p$ if its Newton polygon has one slope. In this article, we prove that the number of irreducible factors of the $n$-th iterate of a pure polynomial…