Related papers: Injectivity of non-singular planar maps with one c…

A conjecture of Miyanishi says that an endomorphism of an algebraic variety, defined over an algebraically closed field of characteristic zero, is an automorphism if the endomorphism is injective outside a closed subset of codimension at…

It is shown that a random $(0,1)$ matrix whose rows are independent random vectors of exactly $n/2$ zero components is non-singular with probability $1-O(n^{-C})$ for any $C>0$. The proof uses a non-standard inverse-type Littlewood-Offord…

A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane curve C with singular point P, we study the…

We consider the problem of neutral inclusions for two-dimensional conductivity and anti-plane elasticity. The neutral inclusion, when inserted in a matrix having a uniform field, does not disturb the field outside the inclusion. The…

A particular orthogonal map on a finite dimensional real quadratic vector space (V,Q) with a non-degenerate quadratic form Q of any signature (p,q) is considered. It can be viewed as a correlation of the vector space that leads to a dual…

Let $1 \le k \le n,$ and let $v_1,\ldots,v_k$ be integral vectors in $\mathbb{Z}^n$. We consider the wedge map $\alpha_{n,k} : (\mathbb{Z}^n)^k /SL_k(\mathbb{Z}) \rightarrow \wedge^k(\mathbb{Z}^n)$, $(v_1,\ldots,v_k) \rightarrow v_1 \wedge…

For a simple Lie algebra $\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we give a characterization of the set of dominant integral weights $\lambda$ such that for any rational point $\mu$ in the fundamental Weyl chamber, $2\lambda-\mu$ is a…

Every automorphism-invariant right non-singular $A$-module is injective if and only if the factor ring of the ring $A$ with respect to its right Goldie radical is a right strongly semiprime ring.

Let $\mathcal{E}$ be the set of endomorphisms of the $n$-torus. We exhibit an example of a map such that is robustly transitive if $\mathcal{E}$ is endowed with the $C^2$ topology but is not robustly transitive if $\mathcal{E}$ is endowed…

We establish the $\#P$-hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing $\lambda$-immanants of $0$-$1$ matrices is $\#P$-hard whenever the…

A non-zero constant Jacobian polynomial maps $F=(P,Q)$ of $\mathbb{C}^2$ is invertible if $P$ and $Q$ are rational polynomials.

An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components with $g \geq 5$, $n \geq 0$. Let $\mathcal{T}(N)$ be the two-sided curve complex of $N$. If $\lambda :\mathcal{T}(N) \rightarrow…

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…

Establishing that a demand mapping is injective is core first step for a variety of methodologies. When a version of the law of demand holds, global injectivity can be checked by seeing whether the demand mapping is constant over any line…

We prove that the image of an isometric embedding into ${\mathbb R}^3$ of a two dimensionnal complete Riemannian manifold $(\Sigma, g)$ without boundary is a convex surface provided both the embedding and the metric $g$ enjoy a…

We propose a handful of definitions of injectivity for a parametrized family of maps and study its link with a global nonuniform stability conjecture for nonautonomous differential systems, which has been recently introduced. This relation…

In the paper, we construct, for $\lambda>0$, complete embedded and non-convex $\lambda$-hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that $\lambda$-hypersurfaces share a common conclusion on the planar…

The Gauss map of a generic immersion of a smooth, oriented surface into $\mathbb R^4$ is an immersion. But this map takes values on the Grassmanian of oriented 2-planes in $\mathbb R^4$. Since this manifold has a structure of a product of…

Let $g:\, [0, 1]\rightarrow [0, 1]$ be piecewise linear unimodal map. We say that $g$ has non-trivial piecewise linear commutator, if there is a continuous piecewise linear $\psi:\, [0, 1]\rightarrow [0, 1]$ such that $g\circ \psi =…