Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

A geomatics-based approach for the derivation of the spatial distribution of sediment transport processes in periglacial mountain environments

Within this paper modern techniques such as satellite image analysis and tools provided by geographic information systems (GIS.) are exploited in order to extend and improve existing techniques for mapping the spatial distribution of sediment transport processes. The processes of interest comprise mass movements such as solifluction, slope wash, dirty avalanches and rock- and boulder falls. They differ considerably in nature and therefore different approaches for the derivation of their spatial extent are required. A major challenge is addressing the differences between the comparably coarse resolution of the available satellite data (Landsat TM/ETM+, 30 in x 30 m) and the actual scale of sediment transport in this environment. A three-stepped approach has been developed which is based on the concept of Geomorphic Process Units (GPUs): parameterization, process area delineation and combination. Parameters include land cover from satellite data and digital elevation model derivatives. Process areas are identified using a hierarchical classification scheme utilizing thresholds and definition of topology. The approach has been developed for the Karkevagge in Sweden and could be successfully transferred to the Rabotsbekken catchment at Okstindan, Norway using similar input data. Copyright (C) 2008 John Wiley & Sons, Ltd.

A Functional Magnetic Resonance Imaging Predictor of Treatment Response to Venlafaxine in Generalized Anxiety Disorder

Background: Functional magnetic resonance imaging (fMRI) holds promise as a noninvasive means of identifying neural responses that can be used to predict treatment response before beginning a drug trial. Imaging paradigms employing facial expressions as presented stimuli have been shown to activate the amygdala and anterior cingulate cortex (ACC). Here, we sought to determine whether pretreatment amygdala and rostral ACC (rACC) reactivity to facial expressions could predict treatment outcomes in patients with generalized anxiety disorder (GAD).Methods: Fifteen subjects (12 female subjects) with GAD participated in an open-label venlafaxine treatment trial. Functional magnetic resonance imaging responses to facial expressions of emotion collected before subjects began treatment were compared with changes in anxiety following 8 weeks of venlafaxine administration. In addition, the magnitude of fMRI responses of subjects with GAD were compared with that of 15 control subjects (12 female subjects) who did not have GAD and did not receive venlafaxine treatment.Results The magnitude of treatment response was predicted by greater pretreatment reactivity to fearful faces in rACC and lesser reactivity in the amygdala. These individual differences in pretreatment rACC and amygdala reactivity within the GAD group were observed despite the fact that 1) the overall magnitude of pretreatment rACC and amygdala reactivity did not differ between subjects with GAD and control subjects and 2) there was no main effect of treatment on rACC-amygdala reactivity in the GAD group.Conclusions: These findings show that this pattern of rACC-amygdala responsivity could prove useful as a predictor of venlafaxine treatment response in patients with GAD.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.