The Brauer group of Sweedler's Hopf algebra

We calculate the Brauer group of the four dimensional Hopf algebra introduced by M. E. Sweedler. This Brauer group is defined with respect to a (quasi-) triangular structure on , given by an element . In this paper is a field . The additive group of is embedded in the Brauer group and it fits in the exact and split sequence of groups: where is the well-known Brauer-Wall group of . The techniques involved are close to the Clifford algebra theory for quaternion or generalized quaternion algebras.

     

A comparison of F-actin labeling methods for light microscopy in different plant specimens: multiple techniques supplement each other

Different detection methods for F-actin labeling were compared on a range of plant specimens: cultured cells, whole organ mounts and sectioned material. For cultured cells, microinjection of labeled phalloidin yielded the most detailed picture but careful permeation methods come close, while immunocytochemical methods always gave relatively poor detail, especially on the level of the fine filaments. For whole organ mounts and sectioned material, permeation methods and immunolocalization are the methods of choice, however never reaching the level of resolution of permeation methods in single cells. It is clear that there is no general and universal good method and multiple techniques are needed, especially when working with different specimens and with different aims.     

The filtering approach to solvent peak suppression in MRS: a critical review

Suppressing the solvent peak is important in many applications of biomedical NMR spectroscopy in order to quantify the metabolites with a great accuracy. Among the postprocessing methods proposed in the literature, many deal with the concept of filtering. However, several proposals lack a theoretical perspective and some have not been explicitly applied to quantification problems. The present article is intended to bridge this gap: five methods are analyzed from a theoretical perspective. Subsequently the different methods are applied to the same set of data, and then the latter are quantified using the model fitting method AMARES. With our set, the scheme proposed by T. Sundin et al. (J. Magn. Reson. 139(2), 189-204 (1999)) proved to be the most reliable method.     

Matrix Continued Fraction for the Resolvent Function of the Band Operator

The aim of this paper is the expansion of a matrix function in terms of a matrix-continued fraction as defined by Sorokin and Van Iseghem. The function under study is the Weyl function or resolvent function of an operator, given in the standard basis by a bi-infinite band matrix, with p subdiagonals and q superdiagonals, where the p + q – 1 intermediate diagonals are zero. The main goal of this paper is to find, for the moments, an explicit form in terms of the coefficients of the continued fraction, called genetic sums, which lead to a generalization of the notion of a Stieltjes continued fraction. These results are extension of some results already found for the vector case (p = 1) and are a step in the direction towards the solution of the direct and inverse spectral problem. The actual computation of the approximants of the given function as the convergents of the continued fraction is shown to be effective. Some possible extensions are considered.     

Uniformly Packed Codes and More Distance Regular Graphs from Crooked Functions

Let V and W be n-dimensional vector spaces over GF(2). A function Q : V W is called crooked (a notion introduced by Bending and Fon-Der-Flaass) if it satisfies the following three properties:

Fonctions séparément harmoniques,un théorème de type Terada

Given D a domain in , G an open set in and E a subset of D verifying the harmonic analogue of Local Polynomial Condition of Leja at some point in D. We prove that if f(x, y) is a complex function defined on D × G such that– f(x, ) is harmonic on G for every fixed x E,– f(, y) is harmonic on D for every fixed y G,then f is harmonic in (x, y) on D × G.     

A conjugated infinite element method for half-space acoustic problems

Many acoustic problems (especially in environmental acoustics) involve half-space domains bounded by a plane subjected to normal admittance boundary conditions. In the "low" frequency domain, the numerical treatment of such problems usually relies on boundary element methods based on a particular Green's function suited for the half-(admittance) plane. In the present paper, an alternative hybrid finite/infinite element scheme is proposed. The method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges (or faces). The procedure is validated through comparisons with an available reference solution.     

Imaging the elastic properties of coiled carbon nanotubes with atomic force microscopy

Coiled carbon nanotubes were produced catalytically by thermal decomposition of hydrocarbon gas. After deposition on a silicon substrate, the three-dimensional structure of the helix-shaped multiwalled nanotubes can be visualized with atomic force microscopy. Helical structures of both chiralities are present in the nanotube deposits. For larger coil diameters ( >170 nm), force modulation microscopy allows one to probe the local elasticity along the length of the coil. Our results agree with the classical theory of elasticity. Similar to the case of straight nanotubes, the Young modulus of coiled multiwalled nanotubes remains comparable to the very high Young modulus of hexagonal graphene sheets.     

Reduction of ECG and gradient related artifacts in simultaneously recorded human EEG/MRI data

Nowadays, electroencephalography signals can be acquired from a patient lying in a magnetic resonance imaging system. It is even possible to acquire EEG signals during an MR imaging sequence. However, such EEG signals are severely distorted by artifacts originating from various effects (e.g., MR gradients, ECG). In this paper, a simple method is presented to reduce such artifacts. Thereby, special attention is focused on artifacts related to the patient's electrocardiogram. The method is shown to be effective, adaptive, and automatic.     

Special designed RF-antenna with integrated non-invasive carbon electrodes for simultaneous magnetic resonance imaging and electroencephalography acquisition at 7T

The construction of a high quality MR RF-antenna with incorporated EEG electrodes for simultaneous MRI and EEG acquisition is presented. The antenna comprises an active decoupled surface coil for receiving the MR signal and a whole body coil for transmitting the excitation RF pulses. The surface coil offers a high signal-to-noise ratio required for fMRI application and the whole body coil has a good B(1) excitation profile, which enables the application of homogeneous RF pulses. Non-invasive carbon electrodes are used in order to minimise the magnetic susceptibility artefacts that occur upon application of conductive materials. This dedicated set-up is compared to a standard set-up being a linear birdcage coil and commercially available Ag/AgCl electrodes. As the acquired EEG signals are heavily disturbed by the gradient switching, intelligent filtering is applied to obtain a clean EEG signal.