Related papers: The von Neumann inequality for 3x3 matrices
This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.
A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess…
In this paper, we study the problem of energy equality for weak solutions of the 3D incompressible non-Newtonian fluid equations with initial value conditions. We derive new sufficient conditions via Sobolev multiplier spaces that guarantee…
Fourier-Motzkin elimination, a standard method for solving systems of linear inequalities, leads to an elementary, short, and self-contained proof of von Neumann's minimax theorem.
Following ideas by Beardon, Minda and Baribeau, Rivard, Wegert in the context of the complex Schwarz-Pick Lemma, we use iterated hyperbolic difference quotients to prove a quaternionic multipoint Schwarz-Pick Lemma, in the context of the…
We investigate proper affine symmetry for the Kantowski-Sachs and Bianchi type III space-times by using holonomy and decomposability, the rank of the 6X6 Riemann matrix and direct integration techniques. It is shown that the very special…
The aim of this note is to give two new conceptual proofs of Ionescu-Weitzenb\"ock's inequality. The first one, which is a vector proof, provides us a geometric interpretation of the difference between the two sides of this inequality and…
In this paper we survey a number of recent results concerning the existence and moduli spaces of solutions of various geometric problems on noncompact manifolds. The three problems which we discuss in detail are: I. Complete properly…
We investigate some well-posedness issues for the initial value problem (IVP) associated to the system \begin{equation} \{ \begin{array} [c]{l} 2i\partial_{t}u+q\partial_{x}^{2}u+i\gamma\partial_{x}^{3}u=F_{1}(u,w)\\…
The Mar\'echal topology, also called the Effros-Mar\'echal topology, is a natural topology one can put on the space of all von Neumann subalgebras of a given von Neumann algebra. It is a result of Mar\'echal from 1973 that this topology is…
We prove that the Riemannian metric on a compact manifold of dimension $n\geq 3$ with smooth boundary can be uniquely determined, up to an isometry fixing the boundary, by the Dirichlet-to-Neumann map associated to the Laplace-Beltrami…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple matrix inequality. As an example application of our four…
We consider the 3 by 3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a question of J. M. Landsberg.
The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The…
In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three…
Three boundary Nevanlinna-Pick interpolation problems at finitely many points are formulated for generalized Schur functions. For each problem, the set of all solutions is parametrized in terms of a linear fractional transformation with a…
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).
In this paper some important inequalities are revisited. First, as motivation, we give another proof of the Hardy's inequality applying convenient vector fields as introduced by Mitidieri, see [6]. Then, we investigate a particular case of…
Thevon Neumann entropy, named after John von Neumann, is an extension of the classical concept of entropy to the field of quantum mechanics. From a numerical perspective, von Neumann entropy can be computed simply by computing all…