Undecidable problems: a sampler

TL;DR: In this paper, it was shown that determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm, approximating an eigen value, eigenvector, singular vector, or the spectral norm is NP-hard and computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.

TL;DR: It is proved that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard and how computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.

TL;DR: In this article, it was shown that the spectral gap problem is undecidable and that the existence or absence of a spectral gap is independent of the axioms of mathematics, which implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless.

TL;DR: We use compact methodologies to verify that DHTs and local-area networks can cooperate to fulfill this aim.

TL;DR: The description for this book, Contributions to the Theory of Games (AM-40), Volume IV, will be forthcoming.

TL;DR: A decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K; by a decision problem for K, we mean the problem of finding a decision algorithm for K.

TL;DR: A review of the collected works of John Tate can be found in this paper, where the authors present two volumes of the Abel Prize for number theory, Parts I, II, edited by Barry Mazur and Jean-Pierre Serre.