Linearly Normal Curves in P^n

2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.

Grading scales for contact lens complications

Purpose. To devise and validate artist-rendered grading scales for contact lens complications Methods. Each of eight tissue complications of contact lens wear (listed under 'Results') was painted by a skilled ophthalmic artist (Terry R. Tarrant) in five grades of severity: 0 (normal), 1 (trace), 2 (mild), 3 (moderate) and 4 (severe). A representative slit lamp photograph of a tissue response of each of the eight complications was shown to 404 contact lens practitioners who had never before used clinical grading scales. The practitioners were asked to grade each tissue response to the nearest 0.1 grade unit by interpolation. Results. The standard deviation (± s.d.) of the 404 responses for each tissue complication is tabulated below:_ing_ 0.5 Endothelial pplymegethisjij-4 0.7 Epithelial microcysts 0.5 Endothelial blebs_ 0.4 Stromal edema_onjunctiva! hyperemia 0.4 Stromal neovascularization 0.4 Papillary conjunctivitis 0.5 The frequency distributions and best-fit normal curves were also plotted. The precision of grading (s.d. x 2) ranged from 0.8 to 1.4, with a mean precision of 1.0. Conclusions. Grading scales afford contact lens practitioners with a method of quantifying the severity of adverse tissue responses to contact lens wear. It is noteworthy that the statistically verified precision of grading (1.0 scale unit) concurs precisely with the essential design feature of the grading scales that each grading step of 1.0 corresponds to clinically significant difference in severity. Thus, as a general rule, a difference or change in grade of > 1.0 can be taken to be both clinically and statistically significant when using these grading scales. Trained observers are likely to achieve even greater grading precision. Supported by Hydron Limited.

Brazos River bar; a study in the significance of grain size parameters

A bar on the Brazos River near Calvert, Texas, has been analyzed in order to determine the geologic meaning of certain grain size parameters and to study the behavior of the size fractions with transport. The bar consists of a strongly bimodal mixture of pebble gravel and medium to fine sand; there is a lack of material in the range of 0.5 to 2 mm, because the source does not supply particles of this size. The size distributions of the two modes, which were established in the parent deposits, are nearly invariant over the bar because the present environment of deposition only affects the relative proportions of the two modes, not the grain size properties of the modes themselves. Two proportions are most common; the sediment either contains no gravel or else contains about 60% gravel. Three sediment types with characteristic bedding features occur on the bar in constant stratigraphic order, with the coarsest at the base. Statistical analysis of the data is based on a series of grain size parameters modified from those of Inman (1952) to provide a more detailed coverage of non-normal size curves. Unimodal sediments have nearly normal curves as defined by their skewness and kurtosis. Non-normal kurtosis and skewness values are held to be the identifying characteristics of bimodal sediments even where such modes are not evident in frequency curves. The relative proportions of each mode define a systematic series of changes in numerical properties; mean size, standard deviation and skewness are shown to be linked in a helical trend, which is believed to be applicable to many other sedimentary suites. The equations of the helix may be characteristic of certain environments. Kurtosis values show rhythmic pulsations along the helix and are diagnostic of two-generation sediments.

Finding the point on Bezier Curves with the normal vector passing an external point

Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.

Size distribution curves of senile plaques in patients with Alzheimer’s disease: do plaques grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and cored senile plaques (SP) were studied in single sections of the temporal lobe from 10 patients with Alzheimer’s disease (AD). The size distribution curves were unimodal and positively skewed. The size distribution curve of the diffuse plaques was shifted towards larger plaques while those of the neuritic and cored plaques were shifted towards smaller plaques. The neuritic/diffuse plaque ratio was maximal in the 11 – 30 micron size class and the cored/ diffuse plaque ratio in the 21 – 30 micron size class. The size distribution curves of the three types of plaque deviated significantly from a log-normal distribution. Distributions expressed on a logarithmic scale were ‘leptokurtic’, i.e. with excess of observations near the mean. These results suggest that SP in AD grow to within a more restricted size range than predicted from a log-normal model. In addition, there appear to be differences in the patterns of growth of diffuse, primitive and cored plaques. If neuritic and cored plaques develop from earlier diffuse plaques, then smaller diffuse plaques are more likely to be converted to mature plaques.

Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces

2000 Mathematics Subject Classification: 14H50.

Effects of dry density and grain size distribution on soil-water characteristic curves of sandy soils

The unsaturated soil mechanics is receiving increasing attention from researchers and as well as from practicing engineers. However, the requirement of sophisticated devices to measure unsaturated soil properties and time consumption have made the geotechnical engineers keep away from implication of the unsaturated soil mechanics for solving practical geotechnical problems. The application of the conventional laboratory devices with some modifications to measure unsaturated soil properties can promote the application of unsaturated soil mechanics into engineering practice. Therefore, in the present study, a conventional direct shear device was modified to measure unsaturated shear strength parameters at low suction. Specially, for the analysis of rain-induced slope failures, it is important to measure unsaturated shear strength parameters at low suction where slopes become unstable. The modified device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying path and wetting path of soil-water characteristic curves (SWCCs) of soils. The results revealed that the internal friction angle of soil was not significantly affected by the suction and as well as the drying-wetting SWCCs of soils. The apparent cohesion of soil increased with a decreasing rate as the suction increased. Further, the apparent cohesion obtained from soil in wetting was greater than that obtained from soil in drying. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as the suction increased. In addition, it was observed that soil became more dilative with the increase of suction. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behaviour than that of in drying at the same net normal stress and the suction.

Spine curvature analysis between participants with obesity and normal weight participants: A biplanar electromagnetic device measurement

To analyse and compare standing thoracolumbar curves in normal weight participants and participants with obesity, using an electromagnetic device, and to analyse the measurement reliability. Material and Methods. Cross-sectional study was carried out. 36 individuals were divided into two groups (normal-weight and participants with obesity) according to their waist circumference. The reference points (T1–T8–L1–L5 and both posterior superior iliac spines) were used to perform a description of thoracolumbar curvature in the sagittal and coronal planes. A transformation from the global coordinate system was performed and thoracolumbar curves were adjusted by fifth-order polynomial equations. The tangents of the first and fifth lumbar vertebrae and the first thoracic vertebra were determined from their derivatives. The reliability of the measurement was assessed according to the internal consistency of the measure and the thoracolumbar curvature angles were compared between groups. Results. Cronbach’s alpha values ranged between 0.824 (95% CI: 0.776–0.847) and 0.918 (95% CI: 0.903–0.949). In the coronal plane, no significant differences were found between groups; however, in sagittal plane, significant differences were observed for thoracic kyphosis. Conclusion. There were significant differences in thoracic kyphosis in the sagittal plane between two groups of young adults grouped according to their waist circumference.

Critical-Behavior Of The Diameters Of Liquid-Liquid Coexistence Curves

We have analyzed the diameters of the liquid–liquid coexistence curves of several binary liquid mixtures in search of the critical anomaly predicted by current theories. We find that while the data are consistent with the predicted functional form, the evidence for such an anomaly is not compelling.

Fluctuation Theory Of The Specific-Heat Of Normal Liquid-3He

The measured specific heat of normal liquid 3He shows a plateau for 0.15<1 K; below 0.15 K and above 1 K, it rises linearly with temperature. However, the slope on the high-temperature side is very much reduced compared with the free-Fermi-gas value. We explain these features through a microscopic, thermal spin- and density-fluctuation model. The plateau is due to spin fluctuations which have a low characteristic energy in 3He. Because of the low compressibility, the density fluctuations are highly suppressed; this leads to a reduced slope for CV(T) for high temperatures.

Bearing Capacity of Clays whose Cohesion Increases Linearly with Depth

Experimental studies (Bishop 1966) show that for saturated normally consolidated clay the cohesion varies linearly with depth. The ultimate bearing capacity in such soil is generally obtained by limit equilibrium and limit analysis methods. Sokolovski's (1960) approach to the method of characteristics is used to find the ultimate bearing capacity of saturated clay whose cohesion is homogeneous and isotropic. In this technical note, the method of characteristics is further developed to determine ultimate bearing capacity of clay whose cohesion varies linearly with depth.

Influence of Osmotic Suction on the Soil-Water Characteristic Curves of Compacted Expansive Clay

Unsaturated clays are subject to osmotic suction gradients in geoenvironmental engineering applications and it therefore becomes important to understand the effect of these chemical concentration gradients on soil-water characteristic curves (SWCCs). This paper brings out the influence of induced osmotic suction gradient on the wetting SWCCs of compacted clay specimens inundated with sodium chloride solutions/distilled water at vertical stress of 6.25 kPa in oedometer cells. The experimental results illustrate that variations in initial osmotic suction difference induce different magnitudes of osmotic induced consolidation and osmotic consolidation strains thereby impacting the wetting SWCCs and equilibrium water contents of identically compacted clay specimens. Osmotic suction induced by chemical concentration gradients between reservoir salt solution and soil-water can be treated as an equivalent net stress component, (p(pi)) that decreases the swelling strains of unsaturated specimens from reduction in microstructural and macrostructural swelling components. The direction of osmotic flow affects the matric SWCCs. Unsaturated specimens experiencing osmotic induced consolidation and osmotic consolidation develop lower equilibrium water content than specimens experiencing osmotic swelling during the wetting path. The findings of the study illustrate the need to incorporate the influence of osmotic suction in determination of the matric SWCCs.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.

Dominance of Radiation Pressure in Ion Acceleration with Linearly Polarized Pulses at Intensities of 10(21) W cm(-2)

A novel regime is proposed where, by employing linearly polarized laser pulses at intensities 10(21) W cm(-2) (2 orders of magnitude lower than discussed in previous work [T. Esirkepov et al., Phys. Rev. Lett. 92, 175003 (2004)]), ions are dominantly accelerated from ultrathin foils by the radiation pressure and have monoenergetic spectra. In this regime, ions accelerated from the hole-boring process quickly catch up with the ions accelerated by target normal sheath acceleration, and they then join in a single bunch, undergoing a hybrid light-sail-target normal sheath acceleration. Under an appropriate coupling condition between foil thickness, laser intensity, and pulse duration, laser radiation pressure can be dominant in this hybrid acceleration. Two-dimensional particle-in-cell simulations show that 1.26 GeV quasimonoenergetic C6+ beams are obtained by linearly polarized laser pulses at intensities of 10(21) W cm(-2).

Normal type Ia supernovae from violent mergers of white dwarf binaries

One of the most important questions regarding the progenitor systems of Type Ia supernovae (SNe Ia) is whether mergers of two white dwarfs can lead to explosions that reproduce observations of normal events. Here we present a fully three-dimensional simulation of a violent merger of two carbon-oxygen white dwarfs with masses of 0.9 M and 1.1 M combining very high resolution and exact initial conditions. A well-tested combination of codes is used to study the system. We start with the dynamical inspiral phase and follow the subsequent thermonuclear explosion under the plausible assumption that a detonation forms in the process of merging. We then perform detailed nucleosynthesis calculations and radiative transfer simulations to predict synthetic observables from the homologously expanding supernova ejecta. We find that synthetic color light curves of our merger, which produces about 0.62 M of Ni, show good agreement with those observed for normal SNe Ia in all wave bands from U to K. Line velocities in synthetic spectra around maximum light also agree well with observations. We conclude that violent mergers of massive white dwarfs can closely resemble normal SNe Ia. Therefore, depending on the number of such massive systems available these mergers may contribute at least a small fraction to the observed population of normal SNe Ia. © 2012 The American Astronomical Society. All rights reserved.