Related papers: On a conjecture by Y. Last

We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951{2001). This approach also indicates some…

We use an upper bound on Jacobsthal's function to complete a proof of a known density result. Apart from the bound on Jacobsthal's function used here, the proof we are completing uses only elementary methods and Dirichlet's theorem on the…

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite…

The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools…

Jacobi's triple product identity is proved from one of Euler's $q$-exponential functions in an elementary way.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

We prove a conjecture of the first author for $GL_2(F)$, where $F$ is a finite extension of $Q_p$.

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".

We prove the Jacobian Conjecture for the space of all the inner functions in the unit disc.

We discuss Jordan's theorem on finite subgroups of invertible matrices and give an account of his original proof.

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…

We present a proof of a conjecture proposed by T. Yano about the generic $b$-exponents of irreducible plane curve singularities.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

We prove a conjecture of H.Widom stated in [W] (math/0108008) about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large Toeplitz determinants. As a byproduct we obtain a new proof of A.Okounkov's…

We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.