Related papers: The Jacobian Conjecture: Approximate roots and int…
There are two main parts in this manuscript. First, for a Jacobian pair $(f, g)$, with the concept of final major roots and final minor roots, we obtain equations and inequalities for intersection numbers ${\rm I}(f_\xi, g)$ and ${\rm…
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…
In [5], without giving a detailed proof, Yamauchi provided a formula to calculate the genus of a certain family of smooth complete intersection algebraic curves. That formula is used extensively in [1] to study the algebraic curves for…
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to $\gcd(deg(P),deg(Q))\le 35$, and…
We give several algorithms addressing computations of intersections of conjugate subgroups.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…
This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective…
Gaussian correlation conjecture states that the Gaussian measure of the intersection of two symmetric convex sets is greater or equal to the product of the measures.
In this paper, we develop the theory of Jacobian rings of open complete intersections, which mean a pair $(X,Z)$ where $X$ is a smooth complete intersection in the projective space and and $Z$ is a simple normal crossing divisor in $X$…
We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of…
The Jacobian conjecture involves the map $y= x - V(x)$ where $y, x$ are n-dimensional vectors, $V(x)$ is a symmetric polynomial of degree $d$ for which the Jacobian hypothesis holds: $ e^{Tr \ln(1- V'(x))} =1,\ \forall x$. The conjecture…
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
In this paper, we study the reciprocal sums of the Jacobsthal numbers. We establish many results on the infinite sum and alternating infinite sum of the reciprocals of Jacobsthal numbers and square Jacobsthal numbers.
The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.…
We present new generalized Jacobson's lemma for generalized Drazin inverses. This extend the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear $\&$ Multilinear Algebra, {\bf 68}(2020), 81--93).
In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian G-space. Our argument closely follows the methods of a 1998 paper of…
It is shown that the $n$-dimensional Jacobian conjecture over algebraic number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is false, then…