Lax Pair Tensors and Integrable Spacetimes

The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation—the three-particle open Toda lattice—is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable.     

Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem

Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral decomposition. A preliminary version of this paper was presented at the AAPM 46th annual meeting, held July 25–29, 2004 in Pittsburgh, PA.     

On minimizing pattern splitting in multi-track string matching

Given a pattern string P=p₁p₂p_m and K parallel text strings over an integer alphabet Σ, our task is to find the smallest integer κ>0 such that P can be split into κ pieces P=P¹…P^κ, where each Pⁱ has an occurrence in some text track T^k_i and these partial occurrences retain the order. We study some variations of this minimum splitting problem, such as splittings with limited gaps and transposition invariance, and show how to use sparse dynamic programming to solve the variations efficiently. In particular, we show that the minimum splitting problem can be interpreted as a shortest path problem on line segments.     

On the structure of space-time caustics

Caustics formed by timelike and null geodesics in a space-timeM are investigated. Care is taken to distinguish the conjugate points in the tangent space (T-conjugate points) from conjugate points in the manifold (M-conjugate points). It is shown that most nonspacelike conjugate points are regular, i.e. with all neighbouring conjugate points having the same degree of degeneracy. The regular timelikeT-conjugate locus is shown to be a smooth 3-dimensional submanifold of the tangent space. Analogously, the regular nullT-conjugate locus is shown to be a smooth 2-dimensional submanifold of the light cone in the tangent space. The smoothness properties of the null caustic are used to show that if an observer sees focusing in all directions, then there will necessarily be a cusp in the caustic. If, in addition, all the null conjugate points have maximal degree of degeneracy (as in the closed Friedmann-Robertson-Walker universes), then the space-time is closed.     

Mass spectrometry of onium compounds—VI: Pyrimidinium oxides

The 5-methyldihydrothiazolo (3,2-c) pyrimidinium cation is evaporated as the corresponding anhydro base. In competition with anhydro base formation the 8-ethoxy derivative eliminates ethyl bromide to give the corresponding betaine. The latter appears to be electronically rearranged and evaporated as a covalent valence isomer. The 3-carboxy derivative investigated suffered decarboxylation and ring opening to a vinyl thione. In the absence of a pyrimidyl methyl group the thiazolo ring was attacked by the anion. The electronically induced fragmentations are discussed and used to deduce the structures of the pyrolytic products.     

Mass spectrometry of pyrylium salts. Free radical evaporation

From ionisation potential measurements it is shown that 2,4,6-triphenylpyrylium and thiopyrylium cations are thermally reduced in the mass spectrometer to the corresponding free radicals during evaporation of the bromides, iodides and fluoroborates. For the fluoroborates minor amounts of a fluoride adduct were also present. Perchlorate salts led to oxidation. The gaseous species from 2,6-diphenyl-4-methylpyrylium iodide consists of the anhydro base and hydrogen iodide.     

All alkoxide route to manganate and coboltate perovskite films and powders: effects of processing parameters

Manganate and cobaltate perovskites having the general formula ABO₃ have many technologically important applications. Here we present all alkoxide based routes to manganate and coboltate perovskite films and nano-phase powders of the compositions; LCMO (La_0.67Ca_0.33MnO₃), LSMO (La_0.75Sr_0.25MnO₃), LNCMO (La_0.33Nd_0.33Ca_0.33MnO₃), LBSMO (La_0.75Ba_0.125Sr_0.125MnO₃) and LSCO (La_0.50Sr_0.50CoO₃). The Mn and Co (oxo) methoxy-ethoxide precursors were prepared by reaction of MnCl₂ or CoCl₂ with 2 Kmoe in methoxy-ethanol-toluene. After hydrolysis of the alkoxide solutions by atmospheric air all systems produced X-ray and electron diffraction amorphous gels of high elemental homogeneity, and the IR spectra showed that they consisted of hydrated oxo-carbonates. Heating in air resulted in similar weight-loss curves for all studied gels passing; loss of H₂O in the range 20–300 °C, decomposition of carbonate groups into oxide and CO₂ in the temperature range 300–700 °C, and in some cases loss of a small amount of oxygen in the temperature range 700–1,000 °C. The pure perovskites were obtained at 690–770 °C with heat rates of typically 5–20 °C min^?1 without annealing. Perovskites could also be obtained at 550 °C by annealing, but these perovskites are prone to be A-site ion inhomogeneous according to the TEM EDS studies, which was not the case for the perovskites heat-treated to at least the carbonate decomposition temperature. This A-site inhomogeneity is ascribed to sequential decomposition of carbonates due to their different thermal stabilities, which is probably a general feature also with other sol–gel precursors and low temperature annealing. High quality polycrystalline films were prepared on Si/SiO₂/TiO₂/Pt substrates with all compositions and high quality epitaxial films were prepared of LCMO (on 100 LaAlO₃) and LSCO (on 100 SrTiO₃). The colossal magneto resistance (CMR) of the epitaxial LCMO films of 32% (246 K) is in parity with PLD derived films. The conductivities of the epitaxial and polycrystalline LSCO films were 1.9 mΩcm (on STO) and 1.7 mΩcm (on α-Al₂O₃, respectively).     

Free radical conformations and conversions in X-irradiated single crystals of L-cysteic acid by electron magnetic resonance and density functional theory studies

Single crystals of L-cysteic acid monohydrate were X-irradiated and studied at 295 K using EPR, ENDOR, and EIE techniques. Three spectroscopically different radicals were observed. These were a deamination radical reduction product (R1), and two oxidation products formed by hydrogen abstraction (radicals R2, R3). R2 and R3 were shown to exhibit the same chemical structure while exhibiting very different geometrical conformations. Cluster DFT calculations at the 6-31G(d,p) level of theory supported the experimental observations for radicals R1 and R2. It was not possible to simulate the R3 radical in any attempted cluster; hence, for this purpose a single molecule approach was used. The precursor radicals for R1, R2, and R3, identified in the low-temperature work on L-cysteic acid monohydrate by Box and Budzinski, were also investigated using DFT calculations. The experimentally determined EPR parameters for the low-temperature decarboxylated cation could only be reproduced correctly within the cluster when the carboxyl group remained in the proximity of the radical. Only one of the two observed low-temperature carboxyl anions (stable at 4 and 48 K) could be successfully simulated by the DFT calculations. Evidence is presented in support of the conclusions that the carboxyl reduction product already is protonated at 4 K and that the irreversible conversion between the two reduction products is brought forward by an umbrella-type inversion of the carboxyl group.     

Conditioning saliva for use in a microfluidic biosensor

This report details an approach to saliva conditioning for compatibility of raw patient samples with microfluidic immunoassay components, principally biosensor surfaces susceptible to fouling. Stimulated whole human saliva spiked with a small molecule analyte (phenytoin, 252 Da) was first depleted of cells, debris and high molecular weight glycoproteins (mucins) using membrane filtration. This process significantly reduced but did not eliminate fouling of biosensor surfaces exposed to the sample. An H-filter, which separates solutes from mixed samples based on their diffusion in laminar flow, was used to extract the analyte from the remaining large molecular weight species in the filtered saliva sample. Patient samples treated in this way retained 23% of the analyte with 97% and 92% reduction in glycoproteins and proteins, respectively, and resulted in 3.6 times less surface fouling than either untreated or filtered saliva alone. These sample conditioning steps will enable the use of fouling-sensitive detection techniques in future studies using clinical saliva samples.     

Incorporation of platinum nanoparticles in ordered mesoporous carbon

Platinum nanoparticles were incorporated within the pore system of ordered mesoporous carbon (OMC) by impregnating the carbon with a water-in-oil (w/o) microemulsion containing dissolved platinum salt followed by reduction of the platinum ions in situ inside the carbon pore system. The procedure provides preparation of metallic nanoparticles from hydrophilic precursors inside the hydrophobic carbon support structure with simultaneous control of the maximum metal particle size. Electron tomography was used to verify the presence of platinum nanoparticles inside the carbon material.