Search results for "Geometry"

Darstellung von Hyperebenen in verallgemeinerten affinen Räumen durch Moduln

1994

The starting point of this article is a generalized concept of affine space which includes all affine spaces over unitary modules. Our main result is a representation theorem for hyperplanes of affine spaces: Every hyperplane which satisfies a weak richness condition is induced by a module. 1

Affine Kettengeometrien �ber Jordanalgebren

1996

It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.

The coordinatization of affine planes by rings

1996

With every unitary free module of rank 2 there is naturally associated a generalized affine plane (e.g. the lines are just the cosets of all nonzero 1-generated submodules). Here we solve the converse problem by coordinatizing a given generalized affine plane which satisfies certain versions of Desargues' postulate.

On the algebraic representation of projectively embeddable affine geometries

1995

The main result of this article is an application of [1] and [2] which yields that an at least 2-dimensional affine geometry is module-induced if and only if it is projectively embeddable into an Arguesian projective lattice geometry.

An axiomatic treatment of ratios in an affine plane

1967

Compensatory strategies in processing facial emotions: evidence from prosopagnosia.

2006

We report data on the processing of facial emotion in a prosopagnosic patient (H.J.A.). H.J.A. was relatively accurate at discriminating happy from angry upright faces, but he performed at chance when the faces were inverted. Furthermore, with upright faces there was no configural interference effect on emotion judgements, when face parts expressing different emotions were aligned to express a new emergent emotion. We propose that H.J.A.'s emotion judgements relied on local rather than on configural information, and this local information was disrupted by inversion. A compensatory strategy, based on processing local face parts, can be sufficient to process at least some facial emotions.

A simplified framework to optimize MRI contrast preparation

2018

PURPOSE This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences. METHODS Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution. RESULTS The proposed approach reduces the computation time of B 0 -robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. …

Hydroxo Hydrido Complexes of Iron and Cobalt (Sn−Fe−Sn, Sn−Co−Sn): Probing Agostic Sn⋅⋅⋅H−M Interactions in Solution and in the Solid State

2000

Bis(toluene)iron 9 reacts with Lappert's stannylene [Sn[CH(SiMe3)2]2] (4) to form the paramagnetic bis-stannylene complex [[(eta6-toluene)Fe-Sn-[CH(SiMe3)2]2]2] (10). Compound 10 reacts with H2O to form the hydroxo hydrido complex [(eta6-C7H8)(mu-OH)(H)-Fe-[Sn[CH(SiMe3)2]2]2] (12) in high yield; its solid-state structure has been elucidated by X-ray and neutron diffraction analysis. In agreement with the 1H NMR results, 12 contains a hydridic ligand whose exact coordination geometry could be determined by neutron diffraction. The 1H and 119Sn NMR analysis of 12 suggested a multicenter Sn/Sn/H/Fe bonding interaction in solution, based on significantly large values of J(Sn,H,Fe) = 640+/-30 Hz…

Products of snowflaked Euclidean lines are not minimal for looking down

2017

We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.

Adaptive BEM for Low Noise Propeller Design

2009

A potential-based Boundary Element Method is presented for the aerodynamic and acoustic design of propel- lers at on- and off-design point conditions. Using an adaptive method, a family of airfoil sections is selected to produce the required performance (thrust, torque and efficiency versus advance ratio) at different cruise flight levels. Climb condi- tions are also considered in order to check the off-design point performance. Once the available airfoil data have been stored in a database, the code processes the families of airfoils to generate a complete geometry for a propeller of the specified performance with an optimized noise emission. The computational scheme adjusts the blade geom…