7,253 research outputs found
Multilevel refinable triangular PSP-splines (Tri-PSPS)
A multi-level spline technique known as partial shape preserving splines (PSPS) (Li and Tian, 2011) has recently been developed for the design of piecewise polynomial freeform geometric surfaces, where the basis functions of the PSPS can be directly built from an arbitrary set of polygons that partitions a giving parametric domain. This paper addresses a special type of PSPS, the triangular PSPS (Tri-PSPS), where all spline basis functions are constructed from a set of triangles. Compared with other triangular spline techniques, Tri-PSPS have several distinctive features. Firstly, for each given triangle, the corresponding spline basis function for any required degree of smoothness can be expressed in closed-form and directly written out in full explicitly as piecewise bivariate polynomials. Secondly, Tri-PSPS are an additive triangular spline technique, where the spline function built from a given triangle can be replaced with a set of refined spline functions built on a set of smaller triangles that partition the initial given triangle. In addition, Tri-PSPS are a multilevel spline technique, Tri-PSPS surfaces can be designed to have a continuously varying levels of detail, achieved simply by specifying a proper value for the smoothing parameter introduced in the spline functions. In terms of practical implementation, Tri-PSPS are a parallel computing friendly spline scheme, which can be easily implemented on modern programmable GPUs or on high performance computer clusters, since each of the basis functions of Tri-PSPS can be directly computed independent of each other in parallel
On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds
In this note we study constant mean curvature surfaces in asymptotically flat
3-manifolds. We prove that, in an asymptotically flat 3-manifold with positive
mass, stable spheres of given constant mean curvature outside a fixed compact
subset are unique. Therefore we are able to conclude that there is a unique
foliation of stable spheres of constant mean curvature in an asymptotically
flat 3-manifold with positive mass.Comment: 22 page
Instantons on General Noncommutative R^4
We study the U(1) and U(2) instanton solutions of gauge theory on general
noncommutative . In all cases considered we obtain explicit results
for the projection operators. In some cases we computed numerically the
instanton charge and found that it is an integer, independent of the
noncommutative parameters .Comment: 14 pages, LaTeX; deleted some confusing statements in the U(1)
1-instanton case, added ref
Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data
This paper is a review on the observational Hubble parameter data that have
gained increasing attention in recent years for their illuminating power on the
dark side of the universe --- the dark matter, dark energy, and the dark age.
Currently, there are two major methods of independent observational H(z)
measurement, which we summarize as the "differential age method" and the
"radial BAO size method". Starting with fundamental cosmological notions such
as the spacetime coordinates in an expanding universe, we present the basic
principles behind the two methods. We further review the two methods in greater
detail, including the source of errors. We show how the observational H(z) data
presents itself as a useful tool in the study of cosmological models and
parameter constraint, and we also discuss several issues associated with their
applications. Finally, we point the reader to a future prospect of upcoming
observation programs that will lead to some major improvements in the quality
of observational H(z) data.Comment: 20 pages, 6 figures, and 1 table, uses REVTeX 4.1. Review article,
accepted by Advances in Astronom
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