Related papers: The Marker-Steinhorn Theorem
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
We expose here a short proof of Cramer's theorem in R based on convex duality.
In this paper we prove gap theorems in Yang-Mills theory for complete four-dimensional manifolds with positive Yamabe constant. We extend the results of Gursky-Kelleher-Streets to complete manifolds. We also describe the equality in the gap…
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
A very short proof of Kneser's theorem via transversal is given.
In this paper, we prove a conjecture of Schnell in the surface case.
We prove Union-Closed sets conjecture.
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
We prove an analog of Lagrange's Theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely many primes. As it is shown the key ingredient for this…
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
Most prime gaps results have been proven using tools from analytic or algebraic number theory in the last few centuries. In this paper, we would like to present some probabilistic way of proving many essential results. A major component of…
We continue to discuss the example presented in \cite{JarPfl2015}. In particular, we clarify some gaps and complete the description of the Shilov boundary.
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.
In this paper we show an index theorem for gerbes
This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's usual proof ends, and stalks it till it ends proving it.