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Planetary Nebulae (PN)
distances represent the fundamental parameter for the determination the
physical properties of the central star of PN. In this paper the distances
scale to Planetary Nebulae in the Galactic bulge were calculated related
to previous distances scales. The proposed distance scale was done by
recalibrated the previous distance scale technique CKS/D82. This scale limited
for nearby PN (D ≤ 3.5 kpc), so the
surface fluxes less than other distance scales. With these criteria the results
showed that the proposed distance scale is more accurate than other scales
related to the observations for adopted sample of PN distances, also the limit
of ionized radius (Rio) for all both optically thick and optically thin in the rang of sizes (0.45
> Rio (pc) > 0.03).
With the advancement in geospatial data acquisition technology, large sizes of digital data are being collected for our world. These include air- and space-borne imagery, LiDAR data, sonar data, terrestrial laser-scanning data, etc. LiDAR sensors generate huge datasets of point of multiple returns. Because of its large size, LiDAR data has costly storage and computational requirements. In this article, a LiDAR compression method based on spatial clustering and optimal filtering is presented. The method consists of classification and spatial clustering of the study area image and creation of the optimal planes in the LiDAR dataset through first-order plane-fitting. First-order plane-fitting is equivalent to the Eigen value problem of the covariance matrix. The Eigen value of the covariance matrix represents the spatial variation along the direction of the corresponding eigenvector. The eigenvector of the minimum Eigen value is the estimated normal vector of the surface formed by the LiDAR point and its neighbors. The ratio of the minimum Eigen value and the sum of the Eigen values approximates the change of local curvature, which determines the deviation of the surface formed by a LiDAR point and its neighbors from the tangential plane formed at that neighborhood. If the minimum Eigen value is close to zero for example, then the surface consisting of the point and its neighbors is a plane. The objective of this ongoing research work is basically to develop a LiDAR compression method that can be used in the future at the data acquisition phase to help remove fake returns and redundant points.
In classical mixed finite element method, the choice of the finite
element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1-Galerkin
mixed finite element method avoids completely the imposition of such a
condition on the approximating spaces. In this article, we discuss and analyze
error estimates for Convection-dominated diffusion problems using H1-Galerkin
mixed finite element method, along with the method of characteristics. Optimal
order of convergence has been achieved for the error estimates of a two-step
Euler backward difference scheme.