Related papers: On the Nakano vanishing theorem

In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.

In this paper, we generalize weak KAM theorem from positive Lagrangian systems to "proper" Hamilton-Jacobi equations. We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the…

In this article, the interplay between Vop\v{e}nka's principle, as well as its weaker counterpart, and presentable $\infty$-categories is studied. Analogous statements, arising after replacing categories with $\infty$-categories in the…

Available data on measured observables allow deriving estimates for some of the phenomenological parameters that characterize the time-evolution and decay of the neutral kaon system based on the hypothesis of complete positivity. The…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We propose a usage of a weak value for a quantum processing between preselection and postselection. While the weak value of a projector of 1 provides a process with certainty like the probability of 1, the weak value of -1 negates the…

A very short proof of Kneser's theorem via transversal is given.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

In this paper, we will provide an alternative definition for the singular Hermitian metric on a vector bundle. Moreover, we discuss the Griffiths and Nakano positivities under this circumstance and prove a generalised Griffiths' vanishing…

In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…

We discuss various recent advances on weak forms of the Twin Prime Conjecture.

We pursue the idea of generalizing Hindman's Theorem to uncountable cardinalities, by analogy with the way in which Ramsey's Theorem can be generalized to weakly compact cardinals. But unlike Ramsey's Theorem, the outcome of this paper is…

In a previous article (arXiv:2111.03143), we generalized Berndtsson's Nakano-positivity by retaining the same consequences under weaker hypotheses. In this article, we propose to further generalize our "twisted" Nakano-positivity theorem to…

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…

In this paper we deal with semilinear problems at resonance. We present a sufficient condition for the existence of a weak solution in terms of the asymptotic properties of nonlinearity. Our condition generalizes the classical…

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be…

The Kodaira-Nakano Vanishing Theorem has been generalized to the relative setting by A. Sommese. We prove a version of this theorem for non-compact manifolds. As an apllication, we prove that the cohomology of a fiber of a symplectic…

We derive the global existence of weak solutions of the Shigesada-Kawasaki-Teramoto systems in space dimension less or equal to 4 with a rather general condition on the coefficients. The existence is established using finite differences in…

We explore the connections between Dickson's lemma and weak Ramsey theory. We show that a weak version of the Paris--Harrington principle for pairs in $c$ colors and miniaturized Dickson's lemma for $c$-tuples are equivalent over…

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.