相关论文: Correction to "Fibers of tropicalization"

We point out an essential gap in the proof of one of main results in \cite{M} and then give a corrected proof for it.

In this note further clue decisive observations on cobweb admissible sequences are shared with the audience. In particular an announced proof of the Theorem 1 (by Dziemia\'nczuk) from [1] announced in India -Kolkata- December 2007 is…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We show that tropicalization of linear series on curves gives rise to two-parameter families of tilings by polymatroids, with one parameter arising from the theory of divisors on tropical curves and the other from the reduction of linear…

In this article, the author provides full details of the proof of the concordance/isotopy problem. The first published proof, [5], accomplished this task only partially since there was an error, see the erratum [6], which damaged the main…

We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness…

A new general all terminal network reliability factorization theorem is stated. We relegate the proof to a forthcoming second part paper.

In this comment we address the preprint of Jha and Hirata (arXiv:1809.10316 [physics.chem-ph]) which claims "Numerical Evidence Falsifying Finite-Temperature Many-Body Perturbation Theory." We agree that finite difference differentiation of…

As recently pointed out by Gabe, a fundamental paper by Elliott and Kucerovsky concerning the absorption theory for C*-algebras contains an error, and as a consequence we must report that Lemma 4.5 in "Classifying C*-algebras with both…

We study anisotropic scaling limits of topological field theories using tropical geometry. The resulting topological field theories are characterized by foliated geometries and are invariant under foliation-preserving gauge transformations.…

In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm…

G\"odel's first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin's incompleteness theorem and a very…

In this note we rectify the proof of Theorem 3.11 in [arXiv:2403.02876]. We also present a set of examples at the end discussing various cases.

It is our aim in this note to give a counter example to an argument used in the proof of the main theorem of the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38…

We present a version of the tropical Nevanlinna theory for real-valued, continuous, piecewise linear functions on the real line. In particular, a tropical version of the second main theorem is proved. Applications to some ultra-discrete…

We give a combinatorial way to locate non-displaceable Lagrangian toric fibers on compact toric manifolds. By taking the intersection of certain tropicalizations coming from combinatorial data of a moment polytope, we locate all strongly…

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

We correct an error in a technical lemma of Drees and Rootz\'en (2010) [arXiv:0910.0343] and discuss consequences for applications.

This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.

This paper has been withdrawn due to a crucial error in the proof of the main theorem