Related papers: A duality proof of Tchakaloff's theorem

We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of degree $m$ for Borel measures with moments up to order $m$. The result improves known results for non-compact supports, since we do not need…

Tchakaloff's theorem from 1957 asserts the existence of exact quadrature rules with non-negative weights for any polynomial space of finite degree on $\mathbb{R}^d$ if the underlying measure is positive, compactly supported, and absolutely…

We prove the existence and uniqueness of measure solutions to the conservative renewal equation and analyze their long time behavior. The solutions are built by using a duality approach. This construction is well suited to apply the…

On metric spaces equipped with doubling measures, we prove that a differentiability theorem holds for Lipschitz functions if and only if the space supports nontrivial (metric) derivations in the sense of Weaver that satisfy an additional…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

Within the framework of the gauge O(1,3)\times O(1,3)-theory, an extension of the Belavin-Polyakov-Schwarz-Tyupkin ansatz is proposed by incorporation there the Levi-Civita tensor. The duality properties of the theory, admitting…

In this paper we give a new proof of a theorem by Alexandrov on the Gauss curvature prescription of Euclidean convex sets. This proof is based on the duality theory of convex sets and on optimal mass transport. A noteworthy property of this…

In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…

In this paper, the $q$-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the $q$-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang…

In this paper, we introduce a new discretization of the Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of some dual cell of a weighted triangulation at the conic singularity. A discrete…

We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the role of the (Lorentzian) modulus of its differential. It is…

In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S.…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

Let $d$ and $k$ be positive integers. Let $\mu$ be a positive Borel measure on $\mathbb{R}^2$ possessing finite moments up to degree $2d-1$. If the support of $\mu$ is contained in an algebraic curve of degree $k$, then we show that there…

Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence…

In this article, we illustrate how the qualitative phase diagram of a gauge theory coupled to matter can be directly proved and how rigorous numerical bounds may be established. Our work reaffirms the seminal result of Fradkin and Shenker…

More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a,b], there exists an n-point quadrature rule (with respect to Lebesgue measure on [a,b]), which is exact for given functions. Here we…

The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the…

We give a version of the Riesz-Haviland theorem for truncated moments problems, characterizing the existence of the representing measures that are absolutely continuous with respect to the Lebesgue measure. The existence of such…

We employ Schauder fixed-point Theorem to prove the existence of at least one positive continuous solution of the quadratic integral equation Moreover, the maximal and the minimal solutions of the last equation are also proved.