Related papers: A counterexample of two Romanov type conjectures
We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.
New cases of the multiplicity conjecture are considered.
Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain…
This paper has been withdrawn by the author due to a crucial error in equation (51).
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We provide a short proof of the 1-dimensional flat chain conjecture.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We present a relative form of the Toponogov comparison theorem.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
We show that the Jacobian conjecture of the two dimensional case is true.
In this paper, we confirm two conjectures proposed by Georgiev, G\'{o}mez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$, thereby providing a complete solution to the de Bruin--Sharma problem. We further…
We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.
This document collects several approaches attempted in proving the Chen-Raspaud Conjecture for k = 3. Each approach is detailed with full proofs and explanations of why it failed. This compilation aims to provide insights and a foundation…
Answering a question of Sakai, we show that the existence of an $\omega_1$-Erd\H{o}s cardinal suffices to obtain the consistency of Chang's Conjecture with $\square_{\omega_1, 2}$. By a result of Donder this is best possible. We also give…
In this paper we disprove three conjectures from [M. Dehmer, F. Emmert-Streib, Y. Shi, Interrelations of graph distance measures based on topological indices, PLoS ONE 9 (2014) e94985] on graph distance measures based on topological indices…
This paper shows that the interpolation theorem fails in the intuitionistic logic of constant domains. This result refutes two previously published claims that the interpolation property holds.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We refute criticisms by Del Santo and Horvat towards our paper "Quantum principle of relativity": most of their counterarguments can be dismissed, and the rest provides further evidence to our claims.