相关论文: Comment on a Paper by Yucai Su On Jacobian Conject…

We study the Jacobian conjecture for Keller maps $f:X_0:=\mathbf{A}^n\rightarrow Y_0:=\mathbf{A}^n$ in characteristic $0$ and attempt to prove it. We are quite aware of the fact that many people have tried to prove the Jacobian conjecture…

We analyze a possible minimal counterexample to the Jacobian Conjecture $P,Q$ with $\gcd(deg(P),deg(Q))=16$ and show that its existence depends only on the existence of solutions for a certain Abel differential equation of the second kind.

In the present paper, we give a proof of the gap-labelling conjecture for quasi-crystals. The main tools are the measured index theorem for laminations and a naturality of the longitudinal Chern character.

The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing…

This paper is the second in a series of two papers which study the phenomenon of tropical split Jacobians. The first paper is a contemplative study, embedded in the broader context of exploring connections between the category of tropical…

We construct a non-proper set of two variables polynomial maps and study the nowhere vanishing Jacobian condition of the Jacobian conjecture for this set. We obtain some classes of polynomial maps satisfying the 2-dimensional Jacobian…

The paper presents a counterexample to the Hodge conjecture.

In the previous paper, we reviewed the Rosenhain's paper to the Jacobi's inversion problem for the genus two hyperelliptic integral. In this paper, we review the G\"{o}pel's paper to the Jacobi's inversion problem for the genus two…

In a previous paper the second author developed a new approach to the abelian p-adic Stark Conjecture at s=1 and stated some related conjectures. This paper develops and applies techniques using p-adic measures and continued fractions to…

Based on many experts' former work in the Jacobian conjecture and an essential analysis of intrinsic topology of linear maps, I completely prove the Jacobian conjecture by demonstrating the injectivity of real Keller map of any…

We prove Atiyah's conjecture for two special types of configurations of N points in the three-dimensional Euclidean space. For one of these types, it is shown that the stronger conjecture of Atiyah and Sutcliffe is valid.

Making use of the theory of infinitesimal canonical transformations, a concise proof is given of Jacobi's identity for Poisson brackets.

In this note, we prove the magnetic spectral gap-labelling conjecture as stated in [arXiv:1508.01064], in all dimensions, for principal solenoidal tori.

The Classical Jacobian Conjecture claims that any unramified endomorphism of a complex affine space is an automorphism. In order to embed this conjecture in a geometric environment, where one could enjoy the beauty and the richness of tools…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

We provide some comments on the article `High-dimensional simultaneous inference with the bootstrap' by Ruben Dezeure, Peter Buhlmann and Cun-Hui Zhang.

A constructive and straightforward proof of the existence of the Zeeman topology is provided, contradicting a fallacious claim contained in the paper "Does Zeeman's Fine Topology Exist?" available at arXiv:1003.3703v1.

The classical honeycomb conjecture asserts that any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling. Pappus discusses this problem in his preface to Book V. This paper…

This comment points out that the recent paper by Maki and Haas [Phys. Rev. B {\bf 67}, 020510 (2003)] is completely wrong.

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…