Slant Factor Research Articles

Warped product lightlike submanifolds with a slant factor

Warped product lightlike submanifolds with a slant factor

Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor

Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor

A Study of Doubly Warped Product Immersions in a Nearly Trans-Sasakian Manifold with Slant Factor

In this article, we discuss the de Rham cohomology class for bislant submanifolds in nearly trans-Sasakian manifolds. Moreover, we give a classification of warped product bislant submanifolds in nearly trans-Sasakian manifolds with some nontrivial examples in the support. Next, it is of great interest to prove that there does not exist any doubly warped product bislant submanifolds other than warped product bislant submanifolds in nearly trans-Sasakian manifolds. Some immediate consequences are also obtained.

Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor

In the present paper, we study some properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and we construct examples in Euclidean spaces. Additionally, we study some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.

Sequential warped product submanifolds having holomorphic, totally real and pointwise slant factors

Sequential warped product submanifolds having holomorphic, totally real and pointwise slant factors

Ionospheric correction for spaceborne single-frequency GPS based on single layer model

A modified ionospheric correction method and the corresponding approximate algorithm for spaceborne single-frequency Global Positioning System (GPS) users are proposed in this study. Single Layer Model (SLM) mapping function for spaceborne GPS was analyzed. SLM mapping functions at different altitudes were calculated. Ionospheric Pierce Point (IPP) trajectories of the dlft station (An IGS station located at the longitude of 4°23′15.22′′E and the latitude of 51°59′9.63′′N, in the TU Delft University, The Netherlands.) and the GRACE satellite were computed with the corresponding single layer height of 350 and 500 km, respectively. The Klobuchar model was used to compute ionospheric delays for the dlft station, and modified Klobuchar model, together with scale factors, was used to compute the fractional ionospheric corrections above the GRACE altitudes. Calculation results were validated using dual-frequency observations. The study shows that the single layer height needs to be changed from 350 to 500 km according to the altitude of GRACE. Approximate forms of Earth angle and slant factor developed for modified Klobuchar model are applicable to GRACE, with accuracy adequate to preserve the essential elements required to compute ionospheric delays. Results show that the Klobuchar model is effective for ground GPS, and the modified Klobuchar model corrects more than 80% on average of the ionospheric delays for spaceborne single-frequency GPS.

Comparison of Ray-Tracing Packages for Troposphere Delays

A comparison campaign to evaluate and compare troposphere delays from different ray-tracing software was carried out under the umbrella of the International Association of Geodesy Working Group 4.3.3 in the first half of 2010 with five institutions participating: the GFZ German Research Centre for Geosciences (GFZ), the Groupe de Recherche de Geodesie Spatiale, the National Institute of Information and Communications Technology (NICT), the University of New Brunswick, and the Institute of Geodesy and Geophysics of the Vienna University of Technology. High-resolution data from the operational analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) for stations Tsukuba (Japan) and Wettzell (Germany) were provided to the participants of the comparison campaign. The data consisted of geopotential differences with respect to mean sea level, temperature, and specific humidity, all at isobaric levels. Additionally, information about the geoid undulations was provided, and the participants computed the ray-traced total delays for 5 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex></formula> elevation angle and every degree in azimuth. In general, we find good agreement between the ray-traced slant factors from the different solutions at 5 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex></formula> elevation if determined from the same pressure level data of the ECMWF. Standard deviations and biases are at the 1-cm level (or significantly better for some combinations). Some of these discrepancies are due to differences in the algorithms and the interpolation approaches. If compared with slant factors determined from ECMWF native model level data, the biases can be significantly larger.

Ray-traced slant factors for mitigating the tropospheric delay at the observation level

Three-dimensional ray tracing through a numerical weather model has been applied to a global precise point positioning (PPP) campaign for modeling both the elevation angle- and azimuth-dependence of the tropospheric delay. Rather than applying the ray-traced slant delays directly, the delay has been parameterized in terms of slant factors, which are applied in a similar manner to traditional mapping functions, but which can account for the azimuthal asymmetry of the delay. Five strategies are considered: (1) Vienna Mapping Functions 1 (VMF1) and estimation of a residual zenith delay parameter; (2) VMF1, estimation of a residual zenith delay and estimation of two tropospheric gradient parameters; (3) three-dimensional ray-traced slant factors and estimation of a residual zenith delay; (4) using only ray-traced slant factors and no estimation of any tropospheric parameters and; (5) using both ray-traced slant factors and estimating a residual zenith delay and two tropospheric gradient parameters. The use of the ray-traced slant factors (solution 3) showed a 3.8% improvement in the repeatability of the up component when compared to the assumption of a symmetric atmosphere (solution 1), while the estimation of two tropospheric gradient parameters gave the best results showing an 7.6% improvement over solution 1 in the up component. Solution 4 performed well in the horizontal domain, allowing for sub-centimeter repeatability but the up component was degraded due to deficiencies in the modeling of the zenith delay, particularly for stations located at equatorial latitudes. The magnitude of the differences in the mean coordinates between solution 2 and solution 3, and the strong correlation with the differences between the north component and the ray-traced gradients (coefficient of correlation of 0.83), as well as the impact of observation geometry on the gradient solution indicate that the use of the ray-traced slant factors could have an implication on the realization of reference frames. The estimated tropospheric products from the PPP solutions were compared to those derived from ray tracing. For the zenith delay, a root mean square (RMS) of 5.4 mm was found, while for the gradient terms, a correlation coefficient of 0.46 for the N–S and 0.42 for the E–W was found for the north–south and east–west components, suggesting that there are still important differences in the gradient parameters which could be due to either errors in the NWM or to non-tropospheric error sources leaking into the PPP-estimated gradients.

Warped product submanifolds of Kaehler manifolds with a slant factor

Recently, we showed that there exist no warped product semi-slant submanifolds in Kaehler manifolds. On the other hand, Carriazo introduced anti-slant submanifolds as a particular class of bi-slant submanifolds. In this paper, we study such submanifolds i

Quantitative differences in arterial morphometry define the placental bed in preeclampsia

The purpose of this study was to quantitatively analyze normal and preeclamptic uteroplacental vasculature. Myometrial arteries from eight placental bed biopsies from uncomplicated term deliveries and 12 from proteinuric preeclampsia were characterized as uteroplacental, spiral, or basal arteries. Basal lumens within 0.2 mm radius and spiral/uteroplacental lumens within 0.4 mm radius were considered as the same artery. The biopsy area, lumen density, and arterial density (after correction for multiple lumens), lumen area, lumen perimeter, mean wall thickness, inflated diameter, and a slant factor, measuring the obliqueness of arterial transection, and ratios of lumen characteristics to mean wall thickness were analyzed. In preeclamptic cases, there were more basal lumens/mm 2 and basal arteries/nun 2 ( P = .003, P = .03), and more spiral lumens/mm 2 and spiral arteries/ mm 2 ( P = .01, P = .03). Basal lumen area ( P = .0003) and wall thickness ( P = .007), and basal and spiral artery lumen perimeters and inflated diameters (for each, P = .0001, P = .048, respectively) and inflated diameter/wall ratios ( P = .04, P = .05) were reduced compared with normal cases. Preeclamptic spiral and basal arteries are more tortuous or densely distributed than normal placental bed arteries, with smaller-caliber lumens and thicker walls. Failure of proper placentation may result in abnormal spatial anatomy in the placental bed. Alternatively, an anatomic variant of spiral and basal arteries may be more susceptible to hemodynamic stresses and endothelial damage and may predispose to preeclampsia.

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The purpose of this study was to quantitatively analyze normal and preeclamptic uteroplacental vasculature. Myometrial arteries from eight placental bed biopsies from uncomplicated term deliveries and 12 from proteinuric preeclampsia were characterized as uteroplacental, spiral, or basal arteries. Basal lumens within 0.2 mm radius and spiral/uteroplacental lumens within 0.4 mm radius were considered as the same artery. The biopsy area, lumen density, and arterial density (after correction for multiple lumens), lumen area, lumen perimeter, mean wall thickness, inflated diameter, and a slant factor, measuring the obliqueness of arterial transection, and ratios of lumen characteristics to mean wall thickness were analyzed. In preeclamptic cases, there were more basal lumens/mm2 and basal arteries/nun2 (P = .003, P = .03), and more spiral lumens/mm2 and spiral arteries/ mm2 (P = .01, P = .03). Basal lumen area (P = .0003) and wall thickness (P = .007), and basal and spiral artery lumen perimeters and inflated diameters (for each, P = .0001, P = .048, respectively) and inflated diameter/wall ratios (P = .04, P = .05) were reduced compared with normal cases. Preeclamptic spiral and basal arteries are more tortuous or densely distributed than normal placental bed arteries, with smaller-caliber lumens and thicker walls. Failure of proper placentation may result in abnormal spatial anatomy in the placental bed. Alternatively, an anatomic variant of spiral and basal arteries may be more susceptible to hemodynamic stresses and endothelial damage and may predispose to preeclampsia.