Unipotent group actions on affine varieties

Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial, $O(X)^{\ast}=k^{\ast},$ and $X//U$ is one-dimensional, it is shown that $O(X)^{U}$=$k[f]$, and if some point in $X$ has trivial isotropy, then $X$ is $U$ equivariantly isomorphic to $U\times A^{1}(k).$ The main results are given distinct geometric and algebraic proofs. Links to the Abhyankar-Sathaye conjecture and a new equivalent formulation of the Sathaye conjecture are made.Comment: 10 pages. This submission comes out of an older submission ("A commuting derivations theorem on UFDs") and contains part of i

Mirror-image relations in category learning

The discrimination of patterns that are mirror-symmetric counterparts of each other is difficult and requires substantial training. We explored whether mirror-image discrimination during expertise acquisition is based on associative learning strategies or involves a representational shift towards configural pattern descriptions that permit resolution of symmetry relations. Subjects were trained to discriminate between sets of unfamiliar grey-level patterns in two conditions, which either required the separation of mirror images or not. Both groups were subsequently tested in a 4-class category-learning task employing the same set of stimuli. The results show that subjects who had successfully learned to discriminate between mirror-symmetric counterparts were distinctly faster in the categorization task, indicating a transfer of conceptual knowledge between the two tasks. Additional computer simulations suggest that the development of such symmetry concepts involves the construction of configural, protoholistic descriptions, in which positions of pattern parts are encoded relative to a spatial frame of reference

A novel collaboratively designed robot to assist carers

© Springer International Publishing Switzerland 2014. This paper presents a co-design process and an assisted navigation strategy that enables a novel assistive robot, Smart Hoist, to aid carers transferring non-ambulatory residents. Smart Hoist was codesigned with residents and carers at IRT Woonona residential care facility to ensure that the device can coexist in the facility, while providing assistance to carers with the primary aim of reducing lower back injuries, and improving the safety of carers and patients during transfers.The Smart Hoist is equipped with simple interfaces to capture user intention in order to provide assisted manoeuvring. Using the RGB-D sensor attached to the device, we propose a method of generating a repulsive force that can be combined with the motion controller’s output to allow for intuitive manoeuvring of the Smart Hoist, while negotiating with the environment.Extensive user trials were conducted on the premises of IRTWoonona residential care facility and feedback from end users confirm its intended purpose of intuitive behaviour, improved performance and ease of use

Coarsening of graded local cohomology

Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.Comment: minor correction

Inducción y utilización de tubérculos in vitro de papa.

Papa-Solanum tuberosu

‘Engage the World’: examining conflicts of engagement in public museums

Public engagement has become a central theme in the mission statements of many cultural institutions, and in scholarly research into museums and heritage. Engagement has emerged as the go-to-it-word for generating, improving or repairing relations between museums and society at large. But engagement is frequently an unexamined term that might embed assumptions and ignore power relationships. This article describes and examines the implications of conflicting and misleading uses of ‘engagement’ in relation to institutional dealings with contested questions about culture and heritage. It considers the development of an exhibition on the Dead Sea Scrolls by the Royal Ontario Museum, Toronto in 2009 within the new institutional goal to ‘Engage the World’. The chapter analyses the motivations, processes and decisions deployed by management and staff to ‘Engage the World’, and the degree to which the museum was able to re-think its strategies of public engagement, especially in relation to subjects,issues and publics that were more controversial in nature

Spin dynamics in molecular ring nanomagnets: Significant effect of acoustic phonons and magnetic anisotropies

The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magnetic ring clusters by fully diagonalizing their microscopic spin Hamiltonians. Whether the nearest-neighbor exchange interaction J is ferromagnetic or antiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may be peaked at around k_B_T=|J| provided the lifetime broadening of discrete energy levels is in proportion to T^3^. Experimental findings for ferromagnetic and antiferromagnetic Cu^II^ rings are reproduced with crucial contributions of magnetic anisotropies as well as acoustic phonons.Comment: 5 pages with 5 figures embedded, to be published in J. Phys. Soc. Jpn. 75, No. 10 (2006

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction

Anisotropy of 4f states in 3d-4f single-molecule magnets

We have measured angular-dependent fluorescence-yield x-ray magnetic circular dichroism spectra on single crystals of the heterometallic 3d-4f 12-metallacrown-4 TbMn4 and DyMn4 complexes. Simulated spectra using crystal-field multiplet calculations reproduce the experimentally observed spectra. The orientation of the molecules causes linear dichroism spectra of the 4f absorption spectra. This natural linear dichroism shows the anisotropic charge distribution of the rare-earth 4f state in the tetragonal crystal field despite the small 4f crystal-field splitting. The magnetic moment of the molecule is dominated by the rare-earth moment revealing a considerably large contribution of orbital moment. From a sum-rule analysis of experimental and simulated x-ray magnetic circular dichroism, we determined corrected spin and orbital Dy moments at low temperature (14 K) within a magnetic field of 7 T. We find a significant angular dependence of the Dy magnetic moments, indicating the presence of fourth-order magnetic anisotropy