The centralizer of a semi-linear transformation

Let V be a finite-dimensional vector space over a division ring D, where D is finite-dimensional over its center F. Suppose T is a semi-linear transformation on V with associated automorphism σ of D. The centralizer of T is the ring C(T) of all linear transformations on V which commute with T. If σ^r is the identity on D for some r ? 1 and no smaller positive power of σ is an inner automorphism, then the center of C(T) is computed to be polynomials in T^r with coefficients from F₀, where F₀ is the subfield of F left elementwise fixed by σ. A matrix version of this theorem is also given.     

The interference of an electron beam with the surface reaction between oxygen and germanium

Electron beam assisted adsorption and desorption of oxygen was studied by Auger electron spectroscopy (AES). Beam assisted adsorption was observed on clean as well as on oxidized surfaces. After an oxygen exposure of 1000 × 10^?7 Torr min and continuous irradiation with beam voltage of 1.5 kV and beam current density 2 microA mm^?2, the oxygen 510 eV signal amplitude from the point of beam impact was 2.5 times greater than the signal from the non-irradiated region. The Ge 89 eV signal showed a corresponding decrease. Enhanced adsorption occurred at beam energies as low as 16.5 eV. After irradiation, the oxidized surface was not carbon contaminated. Following an oxygen exposure of 30 min at 0.1 Torr and 550°C and subsequent additional beam assisted exposure of 1000 × 10^?7 Torr min, the maximum oxide thickness was about 18 Å. Beam assisted desorption did not occur from thin oxygen layers (0–510 eV signal strength less than 5 units, calculated oxide thickness about 6 Å), but occurred from thick oxides and stopped after the signal amplitude had decreased to 5 units. Based on these results, a model for the structure of the oxygen layer covering the Ge(111) surface is proposed. Mechanisms for adsorption and desorption are discussed. The implications of beam assisted adsorption and desorption on electron beam operated surface measurements (LEED, AES, ELS, APS etc.) are stressed.     

The centralizer of a matrix with real quaternion elements

Let T be a Q-endomorphism on a finite dimensional left vector space V over the division ring of real quaternions Q. In this paper we show that the centralizer of T can be regarded as an algebra over the complex numbers C and the dimension of this algebra is computed in terms of the invariant factors of T. Thus the number of C-linearly independent matrices which commute with a given matrix representing T is determined.     

Thiocyanogen (SCN)2− preparation,ultraviolet photoelectron spectrum and structure

The unstable thiocyanogen molecule, (SCN)₂, has been investigated in the gas phase by ultraviolet photoelection spectroscopy. Semi-empincal and ab intio calculations are used to assist with the orbital assignments and to provide an assessment of the structure A disulphide structure, with a dihedral angle of 87.8° is indicated, similar to those of other well known S₂X₂ molecules.     

Zeta potential and electroosmotic mobility in microfluidic devices fabricated from hydrophobic polymers: 1. The origins of charge

This paper combines new experimental data for electrokinetic characterization of hydrophobic polymers with a detailed discussion of the putative origins of charge at water-hydrophobe interfaces. Complexities in determining the origin of charge are discussed in the context of design and modeling challenges for electrokinetic actuation in hydrophobic microfluidic devices with aqueous working fluids. Measurements of interfacial charge are complicated by slip and interfacial water structuring phenomena (see Part 2, this issue). Despite these complexities, it is shown that (i) several hydrophobic materials, such as Teflon and Zeonor, have predictable electrokinetic properties and (ii) electrokinetic data for hydrophobic microfluidic systems is most consistent with the postulate that hydroxyl ion adsorption is the origin of charge.     

Path Boxplots: A Method for Characterizing Uncertainty in Path Ensembles on a Graph

Graphs are powerful and versatile data structures that can be used to represent a wide range of different types of information. In this article, we introduce a method to analyze and then visualize an important class of data described over a graph—namely, ensembles of paths. Analysis of such path ensembles is useful in a variety of applications, in diverse fields such as transportation, computer networks, and molecular dynamics. The proposed method generalizes the concept of band depth to an ensemble of paths on a graph, which provides a center-outward ordering on the paths. This ordering is, in turn, used to construct a generalization of the conventional boxplot or whisker plot, called a path boxplot, which applies to paths on a graph. The utility of path boxplot is demonstrated for several examples of path ensembles including paths defined over computer networks and roads. Supplementary materials for this article are available online.     

Colloidal interactions and transport in nematic liquid crystals

We describe a new nematic liquid-crystal colloid system which is characterized by both charge stabilization of the particles and an interaction force. We estimate the effective charge of the particles by electrophoretic measurements and find that in such systems the director anchoring energy W is very low and the particles have little director distortion around them. The interaction force is created by producing a radial distribution of the nematic order parameter around a locally isotropic region created by ir laser heating. We theoretically describe this as being due to the induced flexoelectric polarization, the quadrupolar symmetry of which provides the required long-range force acting on charged particles.     

Analytic mode matching for a circular dissipative silencer containing mean flow and a perforated pipe

An analytic mode matching scheme that includes higher order modes is developed for a straight-through circular dissipative silencer. Uniform mean flow is added to the central airway and a concentric perforated screen separates the mean flow from a bulk reacting porous material. Transmission loss predictions are compared with experimental measurements and good agreement is demonstrated for three different silencers. Furthermore, it is demonstrated that, when mean flow is present, the axial kinematic matching condition should equate to that chosen for the radial kinematic boundary condition over the interface between the airway and the material. Accordingly, if the radial matching conditions are continuity of pressure and displacement, then the axial matching conditions should also be continuity of pressure and displacement, rather than pressure and velocity as previously thought. When a perforated screen is present the radial pressure condition changes, but the radial kinematic condition should always remain equivalent to that chosen for the axial kinematic matching condition; here, results indicate that continuity of displacement should be retained when a perforated screen is present.     

Gd‐DTPA‐Dopamine‐Bisphytanyl Amphiphile: Synthesis,Characterisation and Relaxation Parameters of the Nanoassemblies and Their Potential as MRI Contrast Agents

Here, a new amphiphilic magnetic resonance imaging (MRI) contrast agent, a Gd^III‐chelated diethylenetriaminepentaacetic acid conjugated to two branched alkyl chains via a dopamine spacer, Gd‐DTPA‐dopamine‐bisphytanyl (Gd‐DTPA‐Dop‐Phy), which is readily capable of self‐assembling into liposomal nanoassemblies upon dispersion in an aqueous solution, is reported. In vitro relaxivities of the dispersions were found to be much higher than Magnevist, a commercially available contrast agent, at 0.47 T but comparable at 9.40 T. Analysis of variable temperature ¹⁷O NMR transverse relaxation measurements revealed the water exchange of the nanoassemblies to be faster than that previously reported for paramagnetic liposomes. Molecular reorientation dynamics were probed by ¹H NMRD profiles using a classical inner and outer sphere relaxation model and a Lipari–Szabo “model‐free” approach. High payloads of Gd^III ions in the liposomal nanoassemblies made solely from the Gd‐DTPA‐Dop‐Phy amphiphiles, in combination with slow molecular reorientation and fast water exchange makes this novel amphiphile a suitable candidate to be investigated as an advanced MRI contrast agent.