Related papers: Vector variational principle

We provide a proof of the $n$-ary Beki\v{c} principle, which states that a vectorial fixpoint of size $n$ can be written in terms of nested fixpoints in each coordinate according to lexicographic order. The proof is inductive.

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend…

It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.

It is shown that Vop\v{e}nka's Principle (VP) can restore almost the entire ZF over a weak fragment of it. Namely, if EST is the theory consisting of the axioms of Extensionality, Empty Set, Pairing, Union, Cartesian Product,…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…

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.

In this note a far extension of the Banach fixed point theorem is proved.

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

We prove the Aharoni Berger Conjecture

The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known qualitative uncertainty principles into quantitative estimates. We then show how to transfer…

The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.

We prove a result on the existence of linear forms of a given Diophantine type.

The existence of the vector supersymmetry is analysed within the context of the finite temperature Chern-Simons theory.

We present a new proof of a primality criterion first proved by Emmanuel Vantieghem.

We prove Burkholder inequality using Bregman divergence.

We give a purely combinatorial proof for the infinitary van der Waerden's theorem.

A very short proof of Kneser's theorem via transversal is given.