Related papers: A simple proof of the representation theorem for b…
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…
Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract…
A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…
This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Although the exposition is aimed at non-experts in set theory,…
We present a new, elementary, dynamical proof of the prime number theorem.
We prove several representation theorems for infinitary predicate modal logic
In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.
A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
We show how one can solve the problem of discriminating between qubit states. We use the quantum state discrimination duality theorem and the Bloch sphere representation of qubits which allows for an easy geometric and analytical…
We determine the representation-finiteness of $A\otimes B$, where both $A$ and $B$ are simply connected algebras with at least three simple modules.
The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
In the seventies, V. G. Drinfeld proved that a moduli problem of deformations by quasi-isogenies of certain $p$-divisible groups with extra actions is representable by an explicit semi-stable model of the $p$-adic symmetric space. This…
We give a simple proof of the Birkhoff theorem about existence of a faithful representation for any finite-dimensional nilpotent Lie algebra of characteristic zero.
Demange (2012) generalized the classical single-crossing property to the intermediate property on median graphs and proved that the representative voter theorem still holds for this more general framework. We complement her result with…
In this note we generalize the Moroianu's fixed point theorem. We propose a very elegant common proof of the Bourbaki's fixed point theorem and our result. We apply our result to give a very elegant proof of the fact that, in the…
Existence theorem is proven for the generating equations of the split involution constraint algebra. The structure of the general solution is established, and the characteristic arbitrariness in generating functions is described.