Related papers: A simple proof of the representation theorem for b…

We present a simple proof of monotonicity for cooperative systems of linear ordinary differential equations, without having recourse to approximation by strongly cooperative systems.

Using the classical Lazard's elimination theorem, we obtain a decomposition theorem for Lie algebras defined by generators and relations of a certain type. This is a preprint version of the paper appearing in Communications in Algebra…

In the existing evidential networks with belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions…

This is a technical report, containing all the theorem proofs and additional evaluations in paper "Monitor Placement for Maximal Identifiability in Network Tomography" by Liang Ma, Ting He, Kin K. Leung, Ananthram Swami, Don Towsley,…

We give a proof of the multi-party typicality conjecture for the first nontrivial case when there are only two parties. The conjecture itself is motivated by the study of multi-party state merging protocols on quantum systems. Our approach…

We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…

The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

The de Rham comparison theorem for varieties, first proved by Faltings, gives the de Rham cohomology of a variety in terms of its p-adic etale cohomology. We extend this theorem to proper, smooth Deligne-Mumford stacks. Two approaches are…

We provide a proof of Sholander's claim (Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3, 369-381 (1952)) concerning the representability of collections of so-called segments by trees, which yields a characterization of…

In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…

We give a short proof of Ahlfors' theorem on covering surfaces.

We provide a simple proof of Kamp's theorem.

We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.

In this short note, we given a new proof of Mitchell's theorem that $L_{T\left(n\right)} K(Z) \cong 0$ for $n \geq 2$. Instead of reducing the problem to delicate representation theory, we use recently established hyperdescent technology…

We provide a short proof of the theorem that every real multivariate polynomial has a symmetric determinantal representation, which was first proved in J. W. Helton, S. A. McCullough, and V. Vinnikov, Noncommutative convexity arises from…

Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…

A direct proof of the Riesz representation theorem is provided. This theorem characterizes the linear functionals acting on the vector space $C(K)$ of continuous functions defined on a compact subset $K$ of the real numbers $\mathbb{R}$.…