Transportation matrices with staircase patterns and majorization

We consider some questions concerning transportation matrices with a certain nonzero pattern. For a given staircase pattern we characterize those row sum vectors R and column sum vectors S such that the corresponding class of transportation matrices with the given row and column sums and the given pattern is nonempty. Two versions of this problem are considered. Algorithms for finding matrices in these matrix classes are introduced and, finally, a connection to the notion of majorization is discussed.     

Influence of HPAM on W/O emulsion separation properties

The present study reports on the influence of partially hydrolyzed polyacrylamide (HPAM) on essential w/o emulsion properties. The characterization has been undertaken with low field NMR to follow droplet sizes and distributions, sedimentation and coalescence kinetic, bench-scale electrocoalescence (E_crit) experiments to follow emulsion stability changes, and electrorheology to detect changes in the viscosity upon applying an external electric field. The result is that HPAM does not basically influence the droplet size distribution (DSD) and the stability level of the emulsions as can be expected of bulk polymers. However, there seems to be an interaction between added demulsifiers either through direct molecular interaction or via an interfacial complexation.     

NMR spectral assignment of 2α- and 3β-methylhopanes and evidence for boat conformation in D ring of 17α(H),21α(H)-hopanes

The full (1)H and (13)C NMR chemical shift assignment of 2α-methyl-17α(H),21β(H)-hopane is presented. This compound is formed in mature sediments from biogenic sources of 2β-methyl-17β(H),21β(H)-hopanoids, which include several cyanobacteria. In addition, full (1)H and (13)C NMR chemical shift data of all four 17,21 isomers of 3β-methylhopane have been assigned. The thermodynamically most stable 3β-configuration corresponds to that found in bacterial sources. The data presented here suggest minor corrections to the (13)C chemical assignments reported earlier for 17α(H)-hopanes. Moreover, spectral evidence indicates an unexpected ring-D boat conformation of 17α(H),21α(H)-hopanes, which may serve to explain the steric strain reported for this isomer.     

3D ultrasound reconstruction algorithms from analog and digital data

Freehand 3D ultrasound is increasingly being introduced in the clinic for diagnostics and image-assisted interventions. Various algorithms exist for combining 2D images of regular ultrasound probes to 3D volumes, being either voxel-, pixel- or function-based. Previously, the most commonly used input to 3D ultrasound reconstruction has been digitized analog video. However, recent scanners that offer access to digital image frames exist, either as processed or unprocessed data. To our knowledge, no comparison has been performed to determine which data source gives the best reconstruction quality. In the present study we compared both reconstruction algorithms and data sources using novel comparison methods for detecting potential differences in image quality of the reconstructed volumes. The ultrasound scanner used in this study was the Sonix RP from Ultrasonix Medical Corp (Richmond, Canada), a scanner that allow third party access to unprocessed and processed digital data. The ultrasound probe used was the L14-5/38 linear probe. The assessment is based on a number of image criteria: detectability of wire targets, spatial resolution, detectability of small barely visible structures, subjective tissue image quality, and volume geometry. In addition we have also performed the more “traditional” comparison of reconstructed volumes by removing a percentage of the input data. By using these evaluation methods and data from the specific scanner, the results showed that the processed video performed better than the digital scan-line data, digital video being better than analog video. Furthermore, the results showed that the choice of video source was more important than the choice of tested reconstruction algorithms.     

Dielectric properties of thin-film ZrO<Subscript>2</Subscript> up to 50 GHz for RF MEMS switches

The dielectric properties of zirconium dioxide (ZrO₂) ceramic thin films were characterized up to 50 GHz using coplanar waveguides (CPWs) and metal–insulator–metal (MIM) capacitors with top circular electrodes. The ZrO₂ films were deposited using a chemical solution onto high-resistivity Si wafers and metal layers. The real part of the dielectric constant of approximately 22 and 26 was extracted at 50 GHz for CPW and MIM structures, respectively, and the loss tangent was approximately 0.09 at 50 GHz. C–V and I–V measurements were carried out to determine low-frequency and DC dielectric properties. The measurement results indicate that ZrO₂ is a promising material to be used as a dielectric layer for radio-frequency (RF) microelectromechanical systems (MEMS) capacitive switches.     

Finite difference representations of non-linear waves

The work concerns cnoidal and solitary wave solutions of the Boussinesq equations in the context of finite difference methods. The existence of permanent wave-forms is discussed and approximate solutions are found for one particular discrete formulation by perturbation techniques. These techniques can be applied to most difference and regular element discretizations of equations describing weakly non-linear and dispersive waves. No proof of convergence of the perturbation expansions is established, but the appropriateness of the solutions is confirmed through comparison with the results of computer simulations. From the perturbation series it is found that the phase speed of solitons is useless for the evaluation of numerical methods and that asymmetries in the discrete equations may ruin the soliton solution. The availability of a discrete closed-form solution is especially important for discussions concerning the existence and accuracy of permanent wave-forms with oblique orientations relative to the grid.     

The Lie Group Structure of the Butcher Group

The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge–Kutta methods. In the present paper, we complement the algebraic treatment of the Butcher group with a natural infinite-dimensional Lie group structure. This structure turns the Butcher group into a real analytic Baker–Campbell–Hausdorff Lie group modelled on a Fréchet space. In addition, the Butcher group is a regular Lie group in the sense of Milnor and contains the subgroup of symplectic tree maps as a closed Lie subgroup. Finally, we also compute the Lie algebra of the Butcher group and discuss its relation to the Lie algebra associated with the Butcher group by Connes and Kreimer.     

Stable rank-2 vector bundles on ℙ3 withc 1=0 andc 2=3

Mathematische Annalen -     

Powered partial least squares discriminant analysis

From the fundamental parts of PLS‐DA, Fisher's canonical discriminant analysis (FCDA) and Powered PLS (PPLS), we develop the concept of powered PLS for classification problems (PPLS‐DA). By taking advantage of a sequence of data reducing linear transformations (consistent with the computation of ordinary PLS‐DA components), PPLS‐DA computes each component from the transformed data by maximization of a parameterized Rayleigh quotient associated with FCDA. Models found by the powered PLS methodology can contribute to reveal the relevance of particular predictors and often requires fewer and simpler components than their ordinary PLS counterparts. From the possibility of imposing restrictions on the powers available for optimization we obtain an explorative approach to predictive modeling not available to the traditional PLS methods. Copyright © 2008 John Wiley & Sons, Ltd.