The point-free relational calculus has been very successful as a language for discussing general programming principles. However, when it comes to speciic applications, the calculus can be rather awkward to use: some things are more clearly and simply expressed using variables. The combination of variables and relational combinators such as converse and choice yields a kind of nondeterministic ...

In a recent paper (Studia Math. 138 (2000) 285–291) we proved pointwise estimates relating some classical maximal and singular integral operators. Here we show that, in a sense, there are more flexible inequalities which not only imply the previously known results but also give something new. In particular, they hold for the multilinear Calderón–Zygmund operators. This result gives a new approa...

Abstract. We derive pointwise a posteriori residual-based error estimates for finite element solutions to the Stokes equations in polyhedral domains. The estimates relies on the regularity of the of Stokes equations and provide an upper bound for the pointwise error in the velocity field on polyhedral domains. Whereas the estimates provide upper bounds for the pointwise error in the gradient of...

Nearest neighbor search aims at obtaining the samples in database with smallest distances from them to queries, which is a basic task range of fields, including computer vision and data mining. Hashing one most widely used methods for its computational storage efficiency. With development deep learning, hashing show more advantages than traditional methods. In this survey, we detailedly investi...

We study the pointwise behavior of perturbations from a viscous shock solution to a scalar conservation law, obtaining an estimate independent of shock strength. We find that for a perturbation with initial data decaying algebraically or slower, the perturbation decays in time at the rate of decay of the integrated initial data in any Lp norm, p ≥ 1. Stability in any Lp norm is a direct consequ...

We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the ...

The paper relates set-valued Lyapunov functions to pointwise asymptotic stability in systems described by a difference inclusion. Pointwise asymptotic stability of a set is a property which requires that each point of the set be Lyapunov stable and that every solution to the inclusion, from a neighborhood of the set, be convergent and have the limit in the set. Weak set-valued Lyapunov function...

We prove that if f is a function belonging to Baire first class on a compact set K/C and each point of K has a (closed) neighborhood where f is the pointwise limit of some sequence of uniformly bounded rational functions, then f on the whole of K is the pointwise limit of a sequence of rational functions uniformly bounded on K. This is an extension of Bishop's localization theorem. As an applic...

We analyze the Stanford Natural Language Inference (SNLI) corpus in an investigation of bias and stereotyping in NLP data. The human-elicitation protocol employed in the construction of the SNLI makes it prone to amplifying bias and stereotypical associations, which we demonstrate statistically (using pointwise mutual information) and with qualitative examples.

Distributional semantic models, deriving vector-based word representations from patterns of word usage in corpora, have many useful applications (Turney and Pantel 2010). Recently, there has been interest in compositional distributional models, which derive vectors for phrases from representations of their constituent words (Mitchell and Lapata 2010). Often, the values of distributional vectors...