Geometric Coefficient Research Articles

Topography-Guided Transepithelial Surface Ablation in the Treatment of Moderate to High Astigmatism.

To analyze the outcomes of treatment of astigmatism of 2.00 diopters (D) or greater with topography-guided transepithelial surface ablation. Retrospective analysis of a series of 206 eyes divided into two groups: myopic astigmatism (153 eyes) and mixed astigmatism (53 eyes). All cases were treated with topography-guided transepithelial surface ablation. Efficacy, safety, and predictability were evaluated, and vector analysis of cylindrical correction was performed. The median preoperative spherical equivalent was -2.63 and -0.63 D for the myopic and mixed astigmatism groups, respectively, with median cylinder of -2.50 D. Postoperative uncorrected distance visual acuity was 20/20 or better in 92% and 83% of eyes in the myopic and mixed astigmatism groups, respectively; the corresponding efficacy indices were 1.00 and 0.96 and residual astigmatism of 0.50 D or less was present in 82.4% and 56.7% of eyes in the myopic and mixed astigmatism groups, respectively. The arithmetic mean magnitude of the difference vector was 0.38 (myopic) and 0.65 (mixed) D. Difference vector magnitude was positively correlated with the magnitude of target induced astigmatism in both groups. The geometric mean coefficient of adjustment index was 1.04 and 1.19, representing undercorrection of 4% and 19% in the myopic and mixed astigmatism groups, respectively. Topography-guided transepithelial ablation is a safe, effective, and predictable treatment for moderate to high astigmatism. [J Refract Surg. 2016;32(6):418-425.].

Extension of thrust network analysis with joints consideration and new equilibrium states

Thrust network analysis is usually applied to form finding of compressive-only structure. In order to study existing structures of historic interest, the joints of the structure need to be taken into account. We study the meaning of the three-dimensional thrust network with respect to the two-dimensional historical concepts of the line of pressure and line of resistance. We propose the refinement of the networks using additional branches with specific properties to widen the set of equilibrium solutions that can be computed. Finally, the application of the method to historic approaches of vault calculation is considered, as well as the convergence of the numerical geometrical coefficient of safety toward Heyman’s geometrical coefficient of safety.

Spatial variation in the 137Cs inventory in soils in a mixed deciduous forest in Fukushima, Japan

The spatial variation of the radiocesium inventory in forest soil was studied c.a. 44 km northwest of the Fukushima Daiichi Nuclear Power Plant, Japan. This study focuses on the effects of canopy interception and downward transfer from the forest canopy to the forest floor via stemflow and throughfall. We established a study plot (400 m2) in the canopy layer of a secondary mixed deciduous forest dominated by Japanese oak (Quercus crispula) and Japanese fir (Abies firma), in August and November 2014. Soil was sampled from 0 to 5 cm depth and 137Cs was measured under the canopy using a 2-m grid and also at the tree trunk bases. We divided the study plot into the five different types of subplot according to the canopy projection areas and the tree species for the analysis. The geometric mean and coefficient of variation of the 137Cs inventory were 202 kBq m−2 and 0.11 (0.52 in the arithmetic coefficient of variation), respectively. Within the forest, the variation in the 137Cs inventory under trees was larger than in crown gap areas. The large spatial variation may be attributed to canopy interception of the initial deposition and downward transfer of radiocesium via stemflow and throughfall.

The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)

A novel multiscale method for multiphase flow in heterogeneous fractured porous media is devised. The discrete fine-scale system is described using an embedded fracture modeling approach, in which the heterogeneous rock (matrix) and highly-conductive fractures are represented on independent grids. Given this fine-scale discrete system, the method first partitions the fine-scale volumetric grid representing the matrix and the lower-dimensional grids representing fractures into independent coarse grids. Then, basis functions for matrix and fractures are constructed by restricted smoothing, which gives a flexible and robust treatment of complex geometrical features and heterogeneous coefficients. From the basis functions one constructs a prolongation operator that maps between the coarse- and fine-scale systems. The resulting method allows for general coupling of matrix and fracture basis functions, giving efficient treatment of a large variety of fracture conductivities. In addition, basis functions can be adaptively updated using efficient global smoothing strategies to account for multiphase flow effects. The method is conservative and because it is described and implemented in algebraic form, it is straightforward to employ it to both rectilinear and unstructured grids. Through a series of challenging test cases for single and multiphase flow, in which synthetic and realistic fracture maps are combined with heterogeneous petrophysical matrix properties, we validate the method and conclude that it is an efficient and accurate approach for simulating flow in complex, large-scale, fractured media.

Cluster automorphism groups of cluster algebras with coefficients

We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. For this, we introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e. the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.

Near‐Source Geometrical Spreading in the Central Virginia Seismic Zone Determined from the Aftershocks of the 2011 Mineral, Virginia, Earthquake

We used aftershocks of the 2011 Mineral, Virginia, earthquake to study geometrical spreading at hypocentral distances less than 60 km in the central Virginia seismic zone. Sixty‐nine aftershocks, occurring from 25 August 2011 through 24 December 2011, provided the data. We used the coda‐normalization method to estimate the attenuation coefficient associated with geometrical spreading. We filtered the time‐domain signals in several octave‐wide frequency bands and examined attenuation of peak S ‐wave amplitude in the 1.0–30.0 Hz frequency range. Amplitude was assumed to decrease as a function of hypocenter distance R according to R − γ . The coefficient of attenuation γ was examined for the three‐component S ‐wave amplitudes, with corrections for SH and SV radiation patterns. We observed no systematic frequency dependence of γ . The coefficient of attenuation for the radial and transverse components, assuming infinite quality factor Q , derived as a weighted mean over the entire range of frequencies (1–30 Hz), are both 1.51±0.05. The weighted mean value of the attenuation coefficient on the vertical component over the same range of frequencies is 1.45±0.05, slightly less than for the horizontal components. We corrected the data assuming three Q models. The estimated geometrical spreading coefficients are in the 1.30–1.46 range, depending on the assumed Q model and component, which is only slightly less than the estimates of γ determined assuming infinite Q . The estimated attenuation coefficients differ significantly from the value of 1.0 expected for a whole space. The results for the horizontal components are in agreement with previous full‐wavefield modeling. However, the observed vertical‐component attenuation is substantially less than that predicted by the synthetics. The depths of the earthquakes are less than 8 km, so these results may not be representative of geometrical spreading in parts of eastern North America where earthquakes occur at greater depths. Online Material: Table of earthquake hypocenters and focal mechanisms.

A chamber study on the reactions of O3, NO, NO2 and selected VOCs with a photocatalytically active cementitious coating material.

Chamber studies were performed to investigate the efficiency of a photocatalytically active cementitious coating material to depollute contaminated air. The results showed a photocatalytic effect on ozone (O3), proven by an increase of the geometric uptake coefficient from 5.2 × 10(-6) for the inactive to 7.7 × 10(-6) for the active material under irradiation. Measured first-order rate constants for nitrogen oxides (NOx) under irradiation are in the range of 2.6-5.9 × 10(-4)s(-1), which is significantly higher compared to the inactive material (7.3-9.7 × 10(-5)s(-1)) demonstrating the photocatalytic effect. However, no significant photocatalytic degradation was observed for the studied volatile organic compounds (VOCs) toluene and isoprene resulting in only an upper limit uptake coefficient of 5.0 × 10(-7) for both VOCs. In all experiments using the photocatalytically active material, a clear formation of small carbonyl (C1-C5) gas phase compounds was identified which is suggested to result from the photocatalytic degradation of organic additives. In contrast to the uptake observed for pure O3, during the experiments with NOx (≥50% relative humidity), a clear photocatalytic formation of O3 was observed. For the material investigated, an empirically derived overall zero-order rate constant of k 0 (O3) ≈ 5 × 10(7)moleculescm(-3)s(-1) was determined. The results demonstrate the necessity of detailed studies of heterogeneous reactions on such surfaces under more complex simulated atmospheric conditions as enabled by simulation chambers.

On a class of functions associated with Sălăgean operator

In this paper we define a new class of analytic functions using the Sălăgean operator and subordination. The geometric significance, radius problem, coefficient estimates and convolution properties have been discussed for functions belonging to this class.

An International Standard for holotranscobalamin (holoTC): international collaborative study to assign a holoTC value to the International Standard for vitamin B12 and serum folate.

Investigation of possible B12 and folate deficiencies requires measurement of these vitamins in serum. There is evidence that holotranscobalamin (holoTC), the active portion of B12 available to cells, is a more specific marker of early B12 deficiency than total B12. The availability of immunoassays for holoTC prompted an international collaborative study to assign a holoTC value to the World Health Organization (WHO) 1st International Standard (IS) for vitamin B12 and serum folate, 03/178. The IS, 03/178, and three serum samples with different holoTC levels were assayed by 12 laboratories in eight countries using manual and automated immunoassays for holoTC; one laboratory additionally performed an in-house assay. Fourteen sets of data were analysed. Overall, the IS, 03/178, and the three serum samples demonstrated assay linearity and parallelism. An overall geometric mean (GM) holoTC value of 106.8 pmol/L was obtained for 03/178, with an inter-laboratory geometric coefficient of variation (GCV) of 10.5%. There was a reduction in inter-laboratory variability when the holoTC levels in the serum samples were determined relative to the IS with an assigned holoTC value rather than to the assays' calibration. Accelerated degradation studies showed that 03/178 was sufficiently stable to serve as an IS for holoTC. The WHO Expert Committee on Biological Standardization endorsed the proposal to assign a holoTC value of 107 pmol/L to 03/178, corresponding to 0.107 pmol per ampoule, for use as the 1st IS for vitamin B12, serum folate, and holoTC.

Variability of recurrence interval and single-event slip for surface-rupturing earthquakes in New Zealand

ABSTRACTRecurrence interval (RI) and single-event slip (SES) for large-magnitude earthquakes that ruptured the ground surface (Mw > 6–7.2) can vary by more than an order of magnitude on individual faults. Frequency histograms, probability density functions (PDFs) and coefficient of variation (Cv, standard deviation/arithmetic mean) values for geological and simulated earthquakes on over 100 New Zealand active faults have been used to quantify RI and SES variability. Histograms of RI and SES for geological paleoearthquakes were constructed using a Monte Carlo method which accounts for the observations and their uncertainties. For the best of the geological PDFs (i.e. ≥7 surface-rupturing events) and earthquake simulations, RI are positively skewed with long recurrence tails (c. three times the mean) which are approximately described by log-normal and Weibull distributions. The geometric mean and coefficient of variation (Cvln) calculated for these log-normal distributions may be up to a factor of two lower and higher, respectively, than those determined assuming a normal distribution. By contrast, SES for geological and simulated earthquakes is often approximately normally distributed and appears to be less variable than RI (RI Cv 0.6 ± 0.2 geological and 0.6 ± 0.3 simulations; SES Cv 0.4 ± 0.2 geological). Variations in earthquake RI and to a lesser extent SES produce order-of-magnitude changes in slip rate over time intervals up to five times the arithmetic mean RI. Quantifying variability of RI, SES and slip rates is important when producing estimates of seismic hazard for surface-rupturing earthquakes, and could be estimated for active faults with poorly constrained paleoearthquake histories using the PDFs presented here.

Variation of transitional functions in multiscale fatigue crack growth of superalloys

Multiscale fatigue crack growth model (MFCGM) can provide better explanation for the multiscale effects on the process of superalloy fatigue. Transitional functions that account for material, loading and geometry effects are incorporated in the MFCGM and play vital role in the proposed model. They are the reflection of the combined microscopic and macroscopic effects. Though validity of transitional functions has been proved in former research, there are still a few critical issues to be clarified. The biggest concern is the assumption of increasing or decreasing trend of transitional curves. It is undeniable that the general trends of these curves agree with the physical phenomena of material degradation, loading restriction and size effects. However, coefficients in transitional functions remain to be specified. Under current circumstance, it is almost impossible to identify these scale parameters. Nevertheless, it is still feasible to employ appropriate coefficients and vary each of the three transitional functions. Variation of transitional functions correspondingly leads to the change of fatigue life of superalloys. Experimental fatigue data of 2024-T3 Al sheets is adopted to modify transitional functions related to material, loading and geometry. Thus the most reasonable and appropriate set of transitional functions are determined. It is found that transitional coefficients ζ η and λ play different role in fatigue crack growth behaviors. Particularly emphasized is the geometric coefficient λ. A set of transitional coefficients are determined such that fatigue crack growth of 2024-T3 Al sheets can be best described and explained. The proposed approach potentially offers the possible reference for engineering safety designs.

Evolution of the rheological and microstructural properties of olivine aggregates during dislocation creep under hydrous conditions

AbstractSince hydrogen plays an important role in dynamic processes in Earth's mantle, we conducted torsion experiments to shear strains of 0.6 to 5.0 on Fe‐bearing olivine aggregates [(Mg0.5Fe0.5)2SiO4: Fo50] under hydrous conditions at T = 1200°C and P = 300 MPa. We deformed samples to high enough strains that a steady state microstructures were achieved, which allowed us to investigate the evolution of both the rheological and microstructural properties. The stress exponent of n ≈ 5.0 and the grain size exponent of p ≈ 0 determined by fitting the strain rate, stress, and grain size data indicate that our samples deformed by dislocation creep. Fourier transform infrared spectroscopy measurements on embedded olivine single crystals demonstrated that our samples were saturated with hydrogen during the deformation experiments. The lattice preferred orientation (LPO) of olivine changes as a function of strain due to competition among three slip systems: (010)[100], (100)[001], and (001)[100]. Observed strain weakening can be attributed to geometrical softening associated with development of LPO, which reduces the stress by ~1/3 from its peak value in constant strain rate experiments. The geometrical softening coefficient determined in this study is an important constraint for modeling and understanding dynamical processes in the upper mantle under hydrous conditions.

Comparability of neuraminidase inhibition antibody titers measured by enzyme-linked lectin assay (ELLA) for the analysis of influenza vaccine immunogenicity

Neuraminidase-inhibition (NI) antibody titers can be used to evaluate the immunogenicity of inactivated influenza vaccines and have provided evidence of serologic cross-reactivity between seasonal and pandemic H1N1 viruses. The traditional thiobarbituric acid assay is impractical for large serologic analyses, and therefore many laboratories use an enzyme-linked lectin assay (ELLA) to determine serum NI antibody titers. The comparability of ELLA NI antibody titers when measured in different laboratories was unknown. Here we report a study conducted through the Consortium for the Standardisation of Influenza SeroEpidemiology (CONSISE) to evaluate the variability of the ELLA. NI antibody titers of a set of 12 samples were measured against both N1 and N2 neuraminidase antigens in 3 independent assays by each of 23 laboratories. For a sample repeated in the same assay, ≥96% of N1 and N2 assays had less than a 4-fold difference in titer. Comparison of the titers measured in assays conducted on 3 different days in the same laboratory showed that a four-fold difference in titer was uncommon. Titers of the same sera measured in different laboratories spanned 3 to 6 two-fold dilutions (i.e., 8–64 fold difference in titer), with an average percent geometric coefficient of variation (%GCV) of 112 and 82% against N1 and N2 antigens, respectively. The difference in titer as indicated by fold range and %GCV was improved by normalizing the NI titers to a standard that was included in each assay. This study identified background signal and the amount of antigen in the assay as critical factors that influence titer, providing important information toward development of a consensus ELLA protocol.

On generalized García-Falset coefficient in Musielak-Orlicz sequence spaces

We introduce a new geometric coefficient which is related Garcia-Falset coefficient and weak star fixed point property. The Garcia-Falset coefficient that was introduced by Benavides in (Houst. J. Math. 22:835-849, 1996) is calculated in this paper for Musielak-Orlicz sequence spaces equipped with the Luxemburg norm. Specifically, in reflexive Banach spaces, the new geometric coefficient and the Garcia-Falset coefficient are the same.

Assessing ocular bulbar redness: a comparison of methods.

We consider whether quantification of ocular bulbar redness, using image processing of relative Red-channel activity (Red-value), can be applied to a clinical sample and how this approach compares to an automated bulbar redness grading technique (Oculus Keratograph 5M, R-scan). Red-values from dry eye patients (n = 25) were determined using image processing of digital photographs over the nasal bulbar conjunctiva. Red-values were compared with subjective grades from six clinicians who graded the images using the IER scale. We considered the level of agreement between the Red-value and automated bulbar redness scores from the commercial instrument (R-scan). Scoring variability for each technique was assessed using the geometric coefficient of variation (gCoV, %). Agreement between techniques was considered with Bland-Altman analyses. Red-values showed a strong linear relationship (R(2) = 0.99) to the R-scan. The Red-value had least variability (gCoV = 0.97%, 95% CI: 0.76-1.35%). The IER grade showed a linear relationship with Red-value (R(2) = 0.99), bound by a floor effect; it did not discriminate changes in redness below a threshold of 1.75 units (Red-value = 33.0%), after which it paralleled the redness returned by the R-scan. Intra-method variability for the redness returned by the R-scan (gCoV = 9.84%, 95% CI: 7.60-13.94%) and IER grades (gCoV = 7.30%, 95% CI: 1.73-10.31%) was similar (p > 0.05). Bland-Altman analysis showed the R-scan was consistently biased towards lower absolute redness scores than the IER. Digital imaging processing, using relative Red-channel activity, was the least variable of the three techniques. The R-scan and IER showed similar intra-observer variability. The linear relationship between R-scan and Red-value suggests that the R-scan could be derived using similar methods.

Automated Tear Film Surface Quality Breakup Time as a Novel Clinical Marker for Tear Hyperosmolarity in Dry Eye Disease

To assess the diagnostic performance of a novel, automated, noninvasive measure of tear film stability derived from Placido disc videokeratography, the tear film surface quality breakup time (TFSQ-BUT), as a clinical marker for diagnosing dry eye disease (DED) relative to a standard of tear hyperosmolarity. This prospective, cross-sectional study involved 45 participants (28 DED, 17 controls). Symptoms (Ocular Surface Disease Index) and signs (tear osmolarity, TFSQ-BUT, tear breakup time measured with sodium fluorescein [NaFl-BUT], ocular surface staining and Schirmer test with topical anesthesia) of DED were assessed. Three measures of TFSQ-BUT and NaFl-BUT were taken per eye; "first," "average," and "shortest" BUT were analyzed separately. Optimal diagnostic cutoff values were determined using the Youden Index. The repeatability and agreement of the TFSQ-BUT was compared with two clinicians who manually assessed noninvasive BUT (CNI-BUT). Repeatability of methods was assessed using the geometric coefficient of variation (gCoV, %). Agreement between methods was considered with Bland-Altman analysis. Eyes with DED had significantly shorter TFSQ-BUTs than controls (P < 0.05). There was a significant, moderate correlation between both shortest and average TFSQ-BUT and NaFl-BUT (r = 0.35, P = 0.02 and r = 0.38, P = 0.01, respectively). The receiver-operator characteristic (ROC) curve for shortest TFSQ-BUT showed an area under the curve of 0.92 (P < 0.0001). Shortest TFSQ-BUT with a criterion of 12.1 seconds had a sensitivity of 82% and specificity of 94% for diagnosing DED against tear hyperosmolarity. Automated TFSQ-BUT showed less variability (gCoV = 9.4%, 95% confidence interval [CI]: 7.1%-14.0%) than CNI-BUT (gCoV = 27.0%, 95% CI: 19.62%-41.06%, P < 0.05). Automated TFSQ-BUT is a repeatable, noninvasive clinical marker with both high sensitivity and specificity for tear hyperosmolarity.

Design of magnetic field configuration for controlled discharge properties in highly ionized plasma

In the present article, the effect of magnetic field design on electron and ion properties in both a metallic Ti/Ar and a reactive Ti/Ar + O2 high power impulse magnetron sputtering (HiPIMS) discharges is investigated. For the purpose, a variable magnetron with defined imbalance and geometrical coefficients K and , respectively, was utilized. The electron density, the mean electron energy, the plasma potential, and the floating potential were determined by employing time-resolved Langmuir probe measurements, for four specified magnetic field configurations. Mass spectroscopy was used in order to determine the energy distribution function of metal (Ti+ , Ti2+) and gaseous (Ar+ , Ar2+ , O+ , O) ions. Analysis of the measured data shows that the magnetic field design dramatically affects the charged particles energy- and spatial-distribution, causing a change in the plasma properties. It is concluded that a well-determined configuration of the magnetic field is necessary in order to insure discharge stability and reproducibility.

Radiative transfer in a semi-transparent medium enclosed in a spherical annulus

The behaviour of the radiative field inside an emitting–absorbing gray and scattering semi-transparent medium at radiative equilibrium, enclosed in a spherical annular cavity bounded by hot and diffusely reflecting surfaces, is described in an exact analytical way. The field at a given point, namely the incident radiation and the radiative flux, is completely characterized by purely geometrical weighting coefficients, which allows determining the temperature field at radiative equilibrium. In this approach, the incident radiation and the radiative flux are expressed as a linear combination of the internal temperatures power 4 at each point of the medium, the coefficients of the combination being the weighting coefficients determined from an analytical way. Some examples show that the proposed method gives perfectly smooth results of high accuracy for both the temperature and flux fields inside the medium.

Analysis of a discontinuous Galerkin method for the bending problem of Koiter shell

We present an analysis for a mixed finite element method for the bending problem of Koiter shell. We derive an error estimate showing that when the geometrical coefficients of the shell mid-surface satisfy certain conditions the finite element method has the optimal order of accuracy, which is uniform with respect to the shell thickness. Generally, the error estimate shows how the accuracy is affected by the shell geometry and thickness. It suggests that to achieve the optimal rate of convergence, the triangulation should be properly refined in regions where the shell geometry changes dramatically. The analysis is carried out for a balanced method in which the normal component of displacement is approximated by discontinuous piecewise cubic polynomials, while the tangential components are approximated by discontinuous piecewise quadratic polynomials, with some enrichments on elements affixed to the shell free boundary. Components of the membrane stress are approximated by continuous piecewise linear functions. We also include a theory of balanced higher order elements and a theory of a simpler lower order method.

Geomorphometric analysis of a rocky coastline: an example from Hornsund, Svalbard

We describe a method to extract a number of quantitative morphometric characteristics of a rocky coastline. The algorithm, which is implemented in the free open-source software GNU Octave, takes as its input an ordered set of coordinate pairs defining the coastline. It finds vertices of specific angularity at two different levels, first approximating convex features (headlands) and then looking for local maxima (embayment edges) in their vicinity. It extracts numerical parameters for each embayment delimited by the former points, including basic geometric parameters (e.g. area, depth and width) and coefficients expressing shapes of embayments (e.g. form factor, coefficient of asymmetry and compactness). These we adapted from morphometric studies of other geomorphic features. Complex headlands and random sectors of the coastline which are delimited by embayment edges are automatically removed. The method was developed and tested on Hornsund in Svalbard, where 20 headlands, 28 embayment edges and 20 embayments were identified, but could be adapted to a wide range of coastal situations. We consider a range of possible applications of the methods, including to the classification of coastlines, change detection and identifying controls on their morphologies, and we discuss the choice of optimum parameters for the algorithm.