Related papers: On two Kuznetsov's conjectures
In this paper the circulant Hadamard conjecture is proved.
We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.
The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.
We prove the boundedness of complements modulo two conjectures: Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.
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…
Akemann and Anderson made a conjecture about ``paving'' projections in finite dimensional matrix algebras which, if true, would settle the well-known Kadison-Singer problem. We falsify their conjecture by an explicit seqence of…
We give an alternative proof for the equivalence of two definitions of the totally positive grassmannian.
We prove Shokurov's index conjecture for quotient singularities.
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
Remarks on mathematical proof and the practice of mathematics.
We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by M. Bertola, B. Dubrovin, D. Yang and by P. Zograf.
We extend two results of Ruzsa and Vu on the additive complements of primes
In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.
We prove Burkholder inequality using Bregman divergence.
We prove some symmetric $q$-congruences.
We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.
We prove Simon's conjecture for 3-manifolds.
We give a more strong heuristic justification of our conjecture on the excess of the odious primes.