Related papers: Existence of the $det^{S^2}$ map

Let K be a field that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analytification V^an of any d-dimensional quasi-projective scheme V over K embeds in…

Harmonic maps from S^2 to S^2 are all weakly conformal, and so are represented by rational maps. This paper presents a study of the L^2 metric gamma on M_n, the space of degree n harmonic maps S^2 -> S^2, or equivalently, the space of…

Let $V$ denote a nonzero finite-dimensional vector space. A tridiagonal pair on $V$ is an ordered pair $A, A^*$ of maps in ${\rm End}(V)$ such that (i) each of $A, A^*$ is diagonalizable; (ii) there exists an ordering $\lbrace V_i…

We show a $2^{n/2+o(n)}$-time algorithm that finds a (non-zero) vector in a lattice $\mathcal{L} \subset \mathbb{R}^n$ with norm at most $\tilde{O}(\sqrt{n})\cdot \min\{\lambda_1(\mathcal{L}), \det(\mathcal{L})^{1/n}\}$, where…

In this paper we consider the topological class, denoted by AV2, of universal covering maps from the plane to the sphere with two removed points. We prove that an element f in AV2 with finite post-singular set is combinatorially equivalent…

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 rational number is dyadic if it has a finite binary representation $p/2^k$, where $p$ is an integer and $k$ is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in…

The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in…

The normal form for an n-dimensional map with irreducible nilpotent linear part is determined using sl2-representation theory. We sketch by example how the reducible case can also be treated in an algorithmic manner. The construction (and…

Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…

An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators…

In this paper we prove the case $dim(V_3)=3$ of a conjecture about the exterior operad ${\Lambda}^{S^2}_{V_d}$. For this we introduce a collection of natural involutions on the set of homogeneous cycle-free $d$-partitions of the complete…

Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm to Mn, where 2<=k<min{m,n}. As a consequence, we give an affirmative answer to Kye's conjecture (also solved independently by Choi) that every…

This paper is a modern exposition of old ideas. The setting is a Euclidian space $E$ of dimension $n$ with associated vector space $V$ of dimension $n$. A (non-zero) sliding vector is a vector in $V$ that is free to move, but only within a…

The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and…

We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.

In this paper we prove the existence of a solution to the Dirichlet problem for harmonic maps into a geodesic ball on which the squared distance function from the origin is strictly convex. This improves a celebrated theorem obtained by S.…

Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…

We introduce a vector-valued version of a uniform algebra, called the vector-valued function space over a uniform algebra. The diameter two properties of the vector-valued function space over a uniform algebra on an infinite compact…

We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between w-spectra with surjective limit projections.