Related papers: A proof of Sendov's conjecture
We show that the Jacobian conjecture of the two dimensional case is true.
We deduce the existence of a maximal irreducibility measure for a Markov chain from Zorn's lemma.
A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
The theory of the on-shell Sudakov form factor to all order of logarithms is explained.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
This paper has been withdrawn by the author due a crucial sign error in Theorem B. We present a geometric proof of Thom conjecture, which uses Khovanov homology. Our approach doesn't use any analytic methods and is quite different from…
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
In this note we prove an inequality involving primes and the product of consecutive primes.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We prove Kontsevich's cyclic formality conjecture.
We present an elementary proof for Ljunggren equation
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.
In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.