Related papers: The choosability version of Brooks' theorem -- a s…
This paper is a continuation of Arai's paper on derivability conditions for Rosser provability predicates. We investigate the limitations of the second incompleteness theorem by constructing three different Rosser provability predicates…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We present an easy proof of Polya's theorem on random walks: with the probability one a random walk on the two-dimensional lattice returns to the starting point.
In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.
This article presents an elementary proof of Zorn's Lemma under the Axiom of Choice, simplifying and supplying necessary details in the original proof by Paul R. Halmos in his book, Naive Set Theory. Also provided, is a preamble to Zorn's…
An equivalent but useful version on the Homological Nerve Theorem is proved.
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
We find some extensions of the Kraft-Russell Generic Equivalence Theorem and using it we obtain a simple proof of a result of Dubouloz and Kishimoto.
Self-similar solutions of the equations for the Burgers hierarchy are presented.
We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson.
We present a short proof of a celebrated result of G\'acs and K\"orner giving sufficient and necessary condition on the joint distribution of two discrete random variables $X$ and $Y$ for the case when their mutual information matches the…
We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
New version, including a variant of Quillen's proof of the Solomon-Tits theorem.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.