Projective geometry and projective metrics,

Bibliography: p. [323]

The Role of Geometry in Wordsworth's "Science of Feelings"

Thesis (Ph.D.)--University of Washington, 2016-06

Geometry and Optimization of Relative Arbitrage

Thesis (Ph.D.)--University of Washington, 2016-06

On the Geometry of Rectifiable Sets with Carleson and Poincare-type inequlaities

Thesis (Ph.D.)--University of Washington, 2016-06

Synthetic, spectroscopic and X-ray crystallographic structural study of the monomeric [Cu(pysme)(sac)(MeOH)] and dimeric [Cu(6mptsc)(sac)](2) complexes [pysme = anion of the pyridine-2-carboxaldehyde Schiff base of S-methyldithiocarbazate, 6mptsc=the anio

New mixed-ligand copper(II) complexes of empirical formulas [Cu(pysme)(sac) (CH3OH)] and [Cu(6mptsc)(sac)](2) have been synthesized and characterized by conductance, magnetic, IR and electronic spectroscopic techniques. X-ray crystallographic structure analyses of these complexes indicate that in both complexes the copper(II) ions adopt a five-coordinate distorted square-pyramidal geometry with an N3SO donor environment. The Schiff bases are coordinated to the copper(II) ions as tridentate NNS chelates via the pyridine nitrogen atom, the azomethine nitrogen atom and the thiolate sulfur atom. In the monomeric [Cu(pysme)(sac)(MeOH)] complex, the saccharinate anion acts as a monodentate ligand coordinating the copper(II) ion via the imino nitrogen atom whereas in the dimeric [Cu(6mptsc)(sac)](2) complex, the sac anion behaves as a bridging bidentate ligand providing the imino nitrogen donor atom to one of the copper(II) ions and the carbonyl oxygen as a weakly coordinated axial ligand atom to the other Cu(II) ion. In both complexes, the copper(II) ions have distorted square-pyramidal environments. The distortion from an ideal square-pyramidal geometry is attributed to the restricted bite angles of the planar tridentate ligand. (C) 2004 Elsevier Ltd. All rights reserved.

Geometric phases of scattering states in a ring geometry: adiabatic pumping in mesoscopic devices

Geometric phases of scattering states in a ring geometry are studied on the basis of a variant of the adiabatic theorem. Three timescales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a ring geometry play a crucial role in determining geometric phases, in contrast to only two timescales, i.e., the adiabatic period and the dwell time, in an open system. We derive a formula connecting the gauge invariant geometric phases acquired by time-reversed scattering states and the circulating (pumping) current. A numerical calculation shows that the effect of the geometric phases is observable in a nanoscale electronic device.

Variability in Cobb angle measurements using reformatted computerized tomography scans

Study Design. Survey of intraobserver and interobserver measurement variability. Objective. To assess the use of reformatted computerized tomography (CT) images for manual measurement of coronal Cobb angles in idiopathic scoliosis. Summary of Background Data. Cobb angle measurements in idiopathic scoliosis are traditionally made from standing radiographs, whereas CT is often used for assessment of vertebral rotation. Correlating Cobb angles from standing radiographs with vertebral rotations from supine CT is problematic because the geometry of the spine changes significantly from standing to supine positions, and 2 different imaging methods are involved. Methods. We assessed the use of reformatted thoracolumbar CT images for Cobb angle measurement. Preoperative CT of 12 patients with idiopathic scoliosis were used to generate reformatted coronal images. Five observers measured coronal Cobb angles on 3 occasions from each of the images. Intraobserver and interobserver variability associated with Cobb measurement from reformatted CT scans was assessed and compared with previous studies of measurement variability using plain radiographs. Results. For major curves, 95% confidence intervals for intraobserver and interobserver variability were +/- 6.6 degrees and +/- 7.7 degrees, respectively. For minor curves, the intervals were +/- 7.5 degrees and +/- 8.2 degrees, respectively. Intraobserver and interobserver technical error of measurement was 2.4 degrees and 2.7 degrees, with reliability coefficients of 88% and 84%, respectively. There was no correlation between measurement variability and curve severity. Conclusions. Reformatted CT images may be used for manual measurement of coronal Cobb angles in idiopathic scoliosis with similar variability to manual measurement of plain radiographs.

Influence of geometry on galvanic corrosion of AZ91D coupled to steel

The influence of geometric factors on the galvanic current density distribution for AZ91D coupled to steel was investigated using experimental measurements and a BEM model. The geometric factors were area ratio of anode/cathode, insulation distance between anode and cathode, depth of solution film covering the galvanic couple and the manner of interaction caused by two independent interacting galvanic couples. The galvanic current density distribution calculated from the BEM model was in good agreement with the experimental measurements. The galvanic current density distribution caused by the interaction of two independent galvanic couples can be reasonably predicted as the linear addition of the galvanic current density caused by each individual galvanic couple. (c) 2005 Elsevier Ltd. All rights reserved.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Quantum computation as geometry

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

Effect of sample geometry on regression rate of the melting interface for carbon steel burned in oxygen

Promoted-ignition testing on carbon steel rods of varying cross-sectional area and shape was performed in high pressure oxygen to assess the effect of sample geometry on the regression rate of the melting interface. Cylindrical and rectangular geometries and three different cross sections were tested and the regression rates of the cylinders were compared to the regression rates of the rectangular samples at test pressures around 6.9 MPa. Tests were recorded and video analysis used to determine the regression rate of the melting interface by a new method based on a drop cycle which was found to provide a good basis for statistical analysis and provide excellent agreement to the standard averaging methods used. Both geometries tested showed the typical trend of decreasing regression rate of the melting interface with increasing cross-sectional area; however, it was shown that the effect of geometry is more significant as the sample's cross sections become larger. Discussion is provided regarding the use of 3.2-mm square rods rather than 3.2-mm cylindrical rods within the standard ASTM test and any effect this may have on the observed regression rate of the melting interface.

Entropy generation for microscale forced convection: effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001

An electrical heart model incorporating real geometry and motion

Abstract—This paper describes an electrical model of the ventricles incorporating real geometry and motion. Cardiac geometry and motion is obtained from segmentations of multipleslice MRI time sequences. A static heart model developed previously is deformed to match the observed geometry using a novel shape registration algorithm. The resulting electrocardiograms and body surface potential maps are compared to a static simulation in the resting heart. These results demonstrate that introducing motion into the cardiac model modifies the ECG during the T wave at peak contraction of the ventricles.

Investigation of the Effect of Array Geometry on the Performance of Free-Space Optical Interconnects

The effect of transmitter and receiver array configurations on the stray-light and diffraction-caused crosstalk in free-space optical interconnects was investigated. The optical system simulation software (Code V) is used to simulate both the stray-light and diffraction-caused crosstalk. Experimentally measured, spectrally-resolved, near-field images of VCSEL higher order modes were used as extended sources in our simulation model. In addition, we have included the electrical and optical noise in our analysis to give more accurate overall performance of the FSOI system. Our results show that by changing the square lattice geometry to a hexagonal configuration, we obtain an overall signal-to-noise ratio improvement of 3 dB. Furthermore, system density is increased by up to 4 channels/mm2.