Related papers: Variational representations for N-cyclically monot…

For any given integer $N\geq 2$, we show that every bounded measurable vector field from a bounded domain $\Omega$ into $\R^d$ is $N$-cyclically monotone up to a measure preserving $N$-involution. The proof involves the solution of a…

We show that any non-degenerate vector field $u$ in $ L^{\infty}(\Omega, \R^N)$, where $\Omega$ is a bounded domain in $\R^N$, can be written as {equation} \hbox{$u(x)= \nabla_1 H(S(x), x)$ for a.e. $x \in \Omega$}, {equation} where $S$ is…

Inspired by a recent result of Funano's, we provide a sharp quantitative comparison result between the first nontrivial eigenvalues of the Neumann Laplacian on bounded convex domains $\Omega_{1} \subset \Omega_{2}$ in any dimension $d$…

Let $\Omega\subset\mathbb{R}^n$, $n\ge 2$, be a bounded connected $C^2$ domain. For any unit vector $\nu\in\mathbb{R}^n$, let $T_{\lambda}^{\nu}=\{x\in\mathbb{R}^n:x\cdot\nu=\lambda\}$,…

We rewrite various lattice Hamiltonian in condensed matter physics in terms of U(2/2) operators that we introduce. In this representation the symmetry structure of the models becomes clear. Especially, the Heisenberg, the supersymmetric t-J…

Let a<b, \Omega=[a,b]^{\Z^d} and H be the (formal) Hamiltonian defined on \Omega by H(\eta) = \frac12 \sum_{x,y\in\Z^d} J(x-y) (\eta(x)-\eta(y))^2 where J:\Z^d\to\R is any summable non-negative symmetric function (J(x)\ge 0 for all…

We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie…

In this note we explicitly construct top-dimensional components of the cyclic convolution varieties. These components correspond (via the geometric Satake equivalence) to irreducible summands $V(\lambda+\mu-N\beta) \subset V(\lambda)…

Convex or concave sequences of $n$ positive terms, viewed as vectors in $n$-space, constitute convex cones with $2n-2$ and $n$ extreme rays, respectively. Explicit description is given of vectors spanning these extreme rays, as well as of…

The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the…

In this note, as a particular case of a more general result, we obtain the following theorem: Let $\Omega\subseteq {\bf R}^n$ be a non-empty bounded open set and let $f:\overline {\Omega}\to {\bf R}^n$ be a continuous function which is…

Suppose that $f$ belongs to a suitably defined complete metric space $ {{\cal C}}^{{\alpha}}$ of H\"older $ {\alpha}$-functions defined on $[0,1]$. We are interested in whether one can find large (in the sense of Hausdorff, or lower/upper…

We study N=2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the Wess-Zumino gauge by harmonic expansions of…

We develop a "metrically selfdual" variational calculus for $c$-monotone vector fields between general manifolds $X$ and $Y$, where $c$ is a coupling on $X\times Y$. Remarkably, many of the key properties of classical monotone operators…

The cycle space of a graph $G$, denoted $C(G)$, is a vector space over ${\mathbb F}_2$, spanned by all incidence vectors of edge-sets of cycles of $G$. If $G$ has $n$ vertices, then $C_n(G)$ is the subspace of $C(G)$, spanned by the…

Let $V$ be a $2n$-dimensional vector space over a field $F$ and $\Omega$ be a non-degenerate symplectic form on $V$. Denote by ${\mathfrak H}_{k}(\Omega)$ the set of all $2k$-dimensional subspaces $U\subset V$ such that the restriction…

Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex potentials. These vector fields are not always derived from…

A Lagrangian definition of a large family of (0,2) supersymmetric conformal field theories may be made by an appropriate gauge invariant combination of a gauged Wess-Zumino-Witten model, right-moving supersymmetry fermions, and left-moving…

Let $\Omega$ be a measurable Euclidean set in $\mathbb{R}^{n}$ that is symmetric, i.e. $\Omega=-\Omega$, such that $\Omega\times\mathbb{R}$ has the smallest Gaussian surface area among all measurable symmetric sets of fixed Gaussian volume.…