Counterexample to Peano's theorem in infinite-dimensional F '-spaces

Let $E$ be a nonnormable Frechet space, and let $E'$ be the space of all continuous linear functionals on $E$ in the strong topology. A continuous mapping $f : E' \to E'$ such that for any $t_0\in R$ and $x_0\in E'$, the Cauchy problem $\dot x= f(x)$, x(t_0) = x_0$ has no solutions is constructed.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

The effect of obstacle position on reach-to-grasp movements

Numerous everyday tasks require the nervous system to program a prehensile movement towards a target object positioned in a cluttered environment. Adult humans are extremely proficient in avoiding contact with any non-target objects (obstacles) whilst carrying out such movements. A number of recent studies have highlighted the importance of considering the control of reach-to-grasp (prehension) movements in the presence of such obstacles. The current study was constructed with the aim of beginning the task of studying the relative impact on prehension as the position of obstacles is varied within the workspace. The experimental design ensured that the obstacles were positioned within the workspace in locations where they did not interfere physically with the path taken by the hand when no obstacle was present. In all positions, the presence of an obstacle caused the hand to slow down and the maximum grip aperture to decrease. Nonetheless, the effect of the obstacle varied according to its position within the workspace. In the situation where an obstacle was located a small distance to the right of a target object, the obstacle showed a large effect on maximum grip aperture but a relatively small effect on movement time. In contrast, an object positioned in front and to the right of a target object had a large effect on movement speed but a relatively small effect on maximum grip aperture. It was found that the presence of two obstacles caused the system to decrease further the movement speed and maximum grip aperture. The position of the two obstacles dictated the extent to which their presence affected the movement parameters. These results show that the antic ipated likelihood of a collision with potential obstacles affects the planning of movement duration and maximum grip aperture in prehension.

Protest practice and (tree) cultures of conflict: understanding the spaces of ‘tree maiming’ in eighteenth- and early nineteenth-century England

Developing understandings of protest and cultures of resistance has been a central theme of the 'new' cultural geography of the 1990s and 2000s. But whilst geographers of the here and now have been highly sensitive to the importance of acts of protest which occur outside of the context of broader social movements, geographers concerned with past protests have tended to focus overwhelmingly upon either understanding the development of social movements or highly specific place-based studies. Through a focus upon the hitherto ignored practice of 'tree maiming', this paper demonstrates not only the value of examining specific protest practices in helping to better understand the complexity of conflict, but also how in periods of acute socio-economic change the evolving relationship between humans and the non-human – in this case trees – is a central discourse to the protest practices of the poor. Such attacks often involved complex cultural understandings about the ways in which trees should – and should not – be socially enrolled.

A three-position spectral line survey of sagittarius B2 between 218 and 263 GHz. II. Data analysis

We present an analysis of the data from our Swedish-ESO Submillimetre Telescope molecular line survey in the 1.3 mm band of the N, M, and NW positions in the Sgr B2 molecular cloud. The line emissions from 42 molecular species, and some of their isotopomers, were analyzed assuming a single temperature and a homogeneous source. In cases where a source size much smaller than the antenna beam (23