We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν, where the Borel measure ν satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When ν = f dx, this condition, which we call D , admits the possibility of f vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when 0 < ...

Voluntary motor actions aim at and are thus governed by predictable action effects. Therefore, representations of an action's effects normally must become activated prior to the action itself. In 5 psychological refractory period experiments the authors investigated whether the activation of such effect representations coincides with the response selection stage of information-processing theori...

The Psychological Refractory Period (PRP) paradigm is a dual-task procedure that can be used to examine the resource demands of specific cognitive processes. Inferences about the underlying processes are typically based on performance in the second of two speeded tasks. If the effect of a factor manipulated in Task 2 decreases as the stimulus onset asynchrony (SOA) between tasks decreases (unde...

In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical case. We show that the convergence of the doubling algorithm is at least linear with rate 1/2. As compared to earlier work on this topic, the results we present here are more gen...

We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.

A large literature on multitasking bottlenecks suggests that people cannot generally make decisions or select responses in two different tasks at the same time. However, these tasks have all involved retrieving preinstructed responses, rather than spontaneously choosing actions based on anticipated hedonic consequences. To assess whether the same bottlenecks encompasses voluntary choices, a gam...

Contents 1. Introduction 1 1.1. Braid monodromy invariants 3 1.2. The degree doubling process 6 1.3. Degree doubling for symplectic Lefschetz pencils 9 2. Stably quasiholomorphic coverings 10 2.1. Quasiholomorphic coverings and braided curves 10 2.2. Stably quasiholomorphic coverings 11 2.3. Proof of Proposition 1 18 3. The degree doubling formula for braid monodromies 21 3.

This paper explains the implications of a mathematical theory (by the same authors) of holes in fractals and their relation to dimension for measurements. The novelty of our approach is to consider the fractal measure on a set rather than just the support of that measure. This should take into account in a more precise way the distribution of data points in measured sets, such as the distributi...

The purpose of this paper is to prove some classical estimates for fractional derivatives of functions defined on a Coifman-Weiss space of homogeneous type. In particular the Product Rule and Chain Rule estimates in [KP] and [CW]. The fractional calculus of M. Riesz was extended to these spaces in [GSV]. Our main tools are fractional difference quotients and the square fractional derivative of ...