Related papers: Consistent maps and their associated dual represen…

We introduce a representation of a 2D steady vector field ${{\mathbf v}}$ by two scalar fields $a$, $b$, such that the isolines of $a$ correspond to stream lines of ${{\mathbf v}}$, and $b$ increases with constant speed under integration of…

A unified approach to the representation of solutions of linear PDE's with constant coefficients in high dimensions in terms of solutions of the same PDE's in lower dimensions is presented. It is based on the observation that if a function…

It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil…

We prove a criterion for continuity of bilinear maps on countable direct sums of topological vector spaces. As a first application, we get a new proof for the fact (due to Hirai et al. 2001) that the map taking a pair of test functions on…

Given a compact p-adic Lie group G over a finite unramified extension L/Q_p let G_0 be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible…

The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…

This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple…

For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also…

Assume that $X$ is a Banach space of measurable functions for which Koml\'os' Theorem holds. We associate to any closed convex bounded subset $C$ of $X$ a coefficient $t(C)$ which attains its minimum value when $C$ is closed for the…

In this survey article we summarize the current state of research in representation stability theory. We look at three different, yet related, approaches, using (1) the category of FI-modules, (2) Schur-Weyl duality, and (3)…

We formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal…

We introduce a common generalization of the strong Hanani-Tutte theorem and the weak Hanani-Tutte theorem: if a graph $G$ has a drawing $D$ in the plane where every pair of independent edges crosses an even number of times, then $G$ has a…

G\"ahler ([4],[5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally…

Let $X$ be a complex smooth algebraic variety admitting a symmetry $L$, that is, an antiholomorphic automorphism of order two. If both, $X$ and $L$ are defined over $\overline{\mathbb Q}$, then Koeck, Lau and Singerman showed the existence…

We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\to Z$ there exists a separately continuous mapping $f:X^2\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\in X$. Under a mild…

Motivated by questions in the study of relative trace formulae, we construct a generalization of Grothendieck's simultaneous resolution over the regular locus of certain symmetric pairs. We use this space to prove a relative version of…

We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and…

In this article we investigate the century-old continuous extension problem of the Riemann map. Let $G$ be a simply connected domain. We call $\lambda$ in $\partial G$ a multiple point if there are simply connected subdomains $ U$ and $V$…

It is well-known that for a surface in a 3-dimensional real space form the constancy of the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true in general for surfaces in an arbitrary 3-dimensional…