相关论文: Centre manifold theorem for maps along manifolds o…

I describe a method, particularly suitable to implementation by computer algebra, for the derivation of low-dimensional models of dynamical systems. The method is systematic and is based upon centre manifold theory. Computer code for the…

The main result is a wall crossing formula for central projections defined on submanifolds of a real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the…

In [8] the authors introduced a pair of new de Rham complexes on a compact oriented Riemannian manifold with boundary by using a pair of new boundary conditions to discuss the refined analytic torsion on a compact manifold with boundary. In…

We introduce a concept that generalizes several different notions of a "centerpoint" in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based…

Dimensionality reduction (DR) and manifold learning (ManL) have been applied extensively in many machine learning tasks, including signal processing, speech recognition, and neuroinformatics. However, the understanding of whether DR and…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

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 introduce the notion of lef line bundles on a complex projective manifold. We prove that lef line bundles satisfy the Hard Lefschetz Theorem, the Lefschetz Decomposition and the Hodge-Riemann Bilinear Relations. We study proper…

Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field…

In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon. We show that usual central finite differences, which are second…

The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mapping in Hausdorff p-vector spaces, and the fixed point theorem for upper semicontinuous set-valued mappings in Hausdorff locally…

We undertake a systematic investigation of compact aspherical manifolds with boundary; motivated by the plethora of examples in the bounded case and by the beauty of the theory in the closed case. Our main theorems give a homological…

The Lefschetz fixed point theorem follows easily from the identification of the Lefschetz number with the fixed point index. This identification is a consequence of the functoriality of the trace in symmetric monoidal categories. There are…

This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.

In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes…

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable…

Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…

In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the…

In this article we prove an existence theorem for coincidence points of mappings in Banach spaces. This theorem generalizes the Kantorovich fixed point theorem.