Research has begun to explore the use of virtual humans (VHs) in clinical interviews (Bickmore, Gruber, & Picard, 2005). When designed as supportive and ‘‘safe’’ interaction partners, VHs may improve such screenings by increasing willingness to disclose information (Gratch, Wang, Gerten, & Fast, 2007). In health and mental health contexts, patients are often reluctant to respond honestly. In th...

It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...

A differential Azumaya algebra, and in particular a differential matrix algebra, over a differential field K with constants C is trivialized by a Picard–Vessiot (differential Galois) extension E. This yields a bijection between isomorphism classes of differential algebras and Picard–Vessiot cocycles Z(G(E/K), PGLn(C)) which cobound in Z (G(E/K), PGLn(E)).

Using Moriwaki’s calculation of the Q-Picard group for the moduli space of curves, I prove the strong Franchetta Conjecture in all characteristics. That is, the canonical class generates the group of rational points on the Picard scheme for the generic curve of genus g ≥ 3. Similar results hold for generic pointed curves.

1 My thanks to Serge Pahaut for our many fruitful discussions together over the past few years. Nathalie Picard and Jean Picard submitted useful suggestions for improving the quality and readability of this paper. Lastly, Kurt van Dender also helped me to improve its presentation.

We present a method to compute the geometric Picard rank of a K3 surface over Q. Contrary to a widely held belief, we show it is possible to verify Picard rank 1 using reduction only at a single prime. Our method is based on deformation theory for invertible sheaves.

We construct full strong exceptional collections of line bundles on smooth toric Fano Deligne-Mumford stacks of Picard number at most two and of any Picard number in dimension two. It is hoped that the approach of this paper will eventually lead to the proof of the existence of such collections on all smooth toric nef-Fano Deligne-Mumford stacks.

Deformation theory requires solving Maurer-Cartan equation (MCE) associated to an DGLA (L-infinity algebra). The universal solution of [HS] is obtained iteratively, as a fixed point of a contraction, analogous to the Picard method. The role of the Kuranishi functor in this construction is emphasized. The parallel with Lie theory suggests that deformation theory is a higher “dimensional” version...

Newton’s method for the incompressible Navier-Stokes equations in IRd gives rise to large sparse non-symmetric indefinite matrices with the general block form ( F B 1 B2 C ) (1) where F has (d × d) blocks and is non-symmetric and in general indefinite. In this work we investigate the performance of two preconditioning techniques introduced for the Picard method for which both proved significant...

In this article, we present a model and a denotational semantics for hybrid systems. Our model is designed to be used for the verification of large, existing embedded applications. The discrete part is modeled by a program written in an extension of an imperative language and the continuous part is modeled by differential equations. We give a denotational semantics to the continuous system insp...