Related papers: A note on the divergence-free Jacobian Conjecture …

For any integer $d \geq 1$, we verify the Jacobian Conjecture for a $d$-linear map in two variables. We prove that almost all the coefficients of the formal inverse are in the ideal specified by the Jacobian condition. We find expressions…

We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for $a_n\equiv 1$, $b_n =-C n^{-\beta}$ ($0<\beta< \frac23)$, one has $d\mu(x)= w(x) dx$ on $(-2,2)$, and near…

We study asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight, which is a weight function with a finite number of algebraic singularities on $[-1,1]$. The recurrence coefficients…

In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small…

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the…

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

Generalized Jacobi polynomials are orthogonal polynomials related to a weight function which is smooth and positive on the whole interval of orthogonality up to a finite number of points, where algebraic singularities occur. The influence…

A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…

We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…

This paper is concerned with the convergence of a two-step modified Newton method for solving the nonlinear system arising from the minimal nonnegative solution of nonsymmetric algebraic Riccati equations from neutron transport theory. We…

In this paper we prove that the generalized version of the Minimal Resolution Conjecture stated by Mustata holds for certain general sets of points on a smooth cubic surface $X \subset \mathbb{P}^3$. The main tool used is Gorenstein liaison…

We show that Lorentz symmetry is generally absent for noncommutative (abelian) gauge theories and obtain a compact formula for the divergence of the Noether currents that allows a throughout study of this instance of symmetry violation. We…

The Jacobi polynomial has been advocated by many authors as a useful tool to evolve non-singlet structure functions to higher $Q^2$. In this work, it is found that the convergence of the polynomial sum is not absolute, as there is always a…

For systems evolving on a Riemannian manifold, we propose converse Lyapunov theorems for asymptotic and exponential stability. The novelty of the proposed approach is that is does not rely on local Euclidean coordinate, and is thus valid on…

We present a conjecture about the asymptotic representation of certain series. The conjecture implies the Riemann hypothesis and it would also indicate the simplicity of the non-trivial zeros of the zeta-function.

In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…

We show that every globally asymptotically stable system with a twice continuously differentiable vector field admits a local polynomial Lyapunov function on an arbitrary bounded neighborhood of the origin.

Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with $T^\times = k^\times$. Then T = S.

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence…