We introduce a pointwise variant of the Assouad dimension for measures on metric spaces, and study its properties in relation to global dimension. show that, general, value may differ from counterpart, but many classical cases, exhibits similar exact dimensionality as local dimension, namely it equals almost everywhere. also prove an explicit formula certain invariant with place-dependent proba...

We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations.

We study pointwise bounds of orthogonal expansions on the real line for a class of exponential weights of smooth polynomial decay at infinity. As a consequence of our main results, we establish pointwise bounds for weighted Hilbert transforms which are of independent interest.

The paper shows that normally hyperbolic one-dimensional compact attractors of smooth dynamical systems are characterized by differential positivity, that is, the pointwise infinitesimal contraction of a smooth cone field. The result is analog to the characterization of zero-dimensional hyperbolic attractors by differential stability, which is the pointwise infinitesimal contraction of a Rieman...

purpose: to report a case who had optic disc duplication, a rare congenital disorder characterized by two well-defined discs in one eye. case report: a 19 months-old child presented with unilateral epiphora in the right eye since birthday. the right eye was smaller than the left eye and mild ptosis was apparent. nasolacrimal duct probing was performed under general anesthesia. the examination r...

A decade ago, Pointwise Circumscription was proposed as a tool for formalizing common sense. In this paper, we revisit some of its uses and examine some cases in which it does not yield the intended behavior. Specifically, we explore the cases in which unsatisfiability may result from the presence of multiple minimal models (for McCarthy’s Circumscription). Then, we present a form of circumscri...

Circumscription is the minimization of predicates subject to restrictions expressed by predicate formulas. We propose a modified notion of circumscription so that, instead of being a single minimality condition, it becomes an “infinite conjun(*tion” of “local” minimality conditions; each of these conditions expresses the impbssibility of changing the value of a predicate from true to f&e at one...