相关论文: Constructive decomposition of functions of two var…

Let $\mathcal{C}$ be a decomposable plane curve over an algebraically closed field $k$ of characteristic 0. That is, $\mathcal{C}$ is defined in $k^2$ by an equation of the form $g(x) = f(y)$, where $g$ and $f$ are polynomials of degree at…

Let P be a finite set of points in general position in the plane. The structure of the complete graph K(P) as a geometric graph includes, for any pair [a,b],[c,d] of vertex-disjoint edges, the information whether they cross or not. The…

We prove that for any open Riemann surface $M$ and any non constant harmonic function $h:M \to \mathbb{R},$ there exists a complete conformal minimal immersion $X:M \to \mathbb{R}^3$ whose third coordinate function coincides with $h.$ As a…

We consider two natural topologies on the space $S(X\times Y,Z)$ of all separately continuous functions defined on the product of two topological spaces $X$ and $Y$ and ranged into a topological or metric space $X$. These topologies are the…

Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some…

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…

For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\times Set$ and use the…

It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…

A functor on compact Hausdorf spaces is constructed as the sum of certain equivariant K-theory groups. It is shown that the functor takes values in lambda-rings and satisfies a Thom isomorphism. In the case that the space is a CW-complex…

This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…

TO APPEAR IN AEQUATIONES MATHEMATICAE - WITHOUT THEOREM 2. THEOREM 2 IS CORRECTLY PROVED IN PREVIOUS VERSIONS 1 AND 2. AUTHOR'S VERSION 3 (WITH A NEW FIGURE 6A) IS UNNECESSARY. Let F \subseteq R denote the field of numbers which are…

Let G be a group, Fin the family of its finite subgroups, and E(G,Fin) the classifying space. Let L^1 be the algebra of trace-class operators in an infinite dimensional, separable Hilbert space over the complex numbers. Consider the…

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative…

We show, for several fake projective planes with nontrivial automorphism group, that the bicanonical map is an embedding.

Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive…

We introduce two notions of a contractive orbit of a set-valued map defined in a first countable space. The first defines the contraction with respect to the topology of the underlying space while the second defines the contraction with…

In the paper we investigate the continuity properties of the mapping $\Phi$ which sends any non-empty compact connected hv-convex planar set $K$ to the associated generalized conic function $f_K$. The function $f_K$ measures the average…

The Helmholtz-Hodge decomposition (HHD) is applied to the construction of Lyapunov functions. It is shown that if a stability condition is satisfied, such a decomposition can be chosen so that its potential function is a Lyapunov function.…

In this article, we derive a common fixed point result for a pair of single valued and set-valued mappings on a metric space having graphical structure. In this case, the set-valued map is assumed to be closed valued instead of closed and…

In this paper we prove FG-coupled fixed point theorems for different contractive mappings and generalized quasi- contractive mappings in partially ordered complete metric spaces. We prove the existence of FG-coupled fixed points of…