Related papers: Borel Conjecture and Dual Borel Conjecture
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
We prove the Aharoni Berger Conjecture
The article presents the proof of Casas-Alvero conjecture.
We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.
We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.
We provide new sufficient conditions under which Ryser's conjecture holds.
We provide a proof of the Borwein Conjecture using analytic methods.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
We show that the Jacobian conjecture of the two dimensional case is true.
In this paper we prove the WALA conjecture.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
In this paper the circulant Hadamard conjecture is proved.
We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…
We prove Union-Closed sets conjecture.
Several results about the union-closed sets conjecture are presented.
In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.
We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.