Related papers: A Note on the Koethe Conjecture

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.

In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.

Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of…

We give a minimal counterexample for a conjecture of Ross and Yong (2015) which proposes a K-Kohnert rule for Grothendieck polynomials. We conjecture a revised version of this rule. We then prove both rules hold in the $321$-avoiding case.

In the preprint of 1993 the author formulated some conjectures on monotonicity of ratios for exponential series remainders. They are equivalent to conjectures on monotonicity of a ratio of Kummer hypergeometric functions and presumably not…

In this note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal . As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.

Let X be the quotient of a smooth projective variety over a field by a finite group action (in which case we say X is pseudo-smooth), such that the singularities of X are isolated k-rational points. Let Y be obtained by blowing up these…

We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.

In this note, we present two arguments showing that the classical \textit{linear adjoint cone restriction conjecture} holds for the class of functions supported on the cone and invariant under the spatial rotation in all dimensions. The…

We deny with a concrete example the generality of the correlation subadditivity relation conjectured by Modi et al's [Phys. Rev. Lett. {\bf 104}, 080501 (2010)] for any quantum state and point out that the correlation additivity relation is…

In this article, we give two different proofs of why the Collatz Conjecture is false.

We study an analogue of the Mertens conjecture in the setting of global function fields. Building on the work of Cha, we show that most hyperelliptic curves do not satisfy the Mertens conjecture, but that if we modify the Mertens conjecture…

In this paper, we prove that Gorenstein projective conjecture is left and right symmetric and the co-homology vanishing condition can not be reduced in general. Moreover, the Gorenstein projective conjecture is proved to be true for…

In this short note, we show that the assumption "convex" in Theorem 7 of Brendle-Eichmair's paper \cite{BE} is unnecessary.

We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.