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91.
The overlay of 2≤m≤d minimization diagrams of n surfaces in ℝ
d
is isomorphic to a substructure of a suitably constructed minimization diagram of mn surfaces in ℝ
d+m−1. This elementary observation leads to a new bound on the complexity of the overlay of minimization diagrams of collections
of d-variate semi-algebraic surfaces, a tight bound on the complexity of the overlay of minimization diagrams of collections of
hyperplanes, and faster algorithms for constructing such overlays. Further algorithmic implications are discussed.
Work by V. Koltun was supported by NSF CAREER award CCF-0641402.
Work by M. Sharir was supported by NSF Grants CCR-00-98246 and CCF-05-14079, by a grant from the Israeli Academy of Sciences
for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski Minerva Center for
Geometry at Tel Aviv University. 相似文献
92.
The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic
α
-stable process with parameter m on ℝ
d
space. This process has an infinitesimal generator of the form mI–(m
2/α
I–Δ)
α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing
was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide
two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates
known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting
Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space.
The main result states that the Green function is comparable with the Green function for the Brownian motion if the points
are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points
the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough.
Research supported by KBN Grants. 相似文献
93.
We show that n lines in 3-space can be cut into
O(n2-1/69log16/69n) pieces, such that all depth cycles
defined by triples of lines are eliminated. This partially resolves
a long-standing open problem in computational geometry, motivated by
hidden-surface removal in computer graphics. 相似文献
94.
We study subgroups of ℤℕ which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger
(1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely
combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of
Babinkostova, Kočinac, and Scheepers.
The first author was supported by the EU Research and Training Network HPRN-CT-2002-00287.
The second author was partially supported by the Koshland Center for Basic Research. 相似文献
95.
On the performance of the ICP algorithm 总被引:2,自引:0,他引:2
We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not. 相似文献
96.
We became aware, in the course of our on-going research, that the number-average molecular weight of poly(1,4-trans isoprene) determined by conventional gel permeation chromatography (GPC) in tetrahydrofuran (THF) using polystyrene standards differs from its true value by a factor 2. As far as we know, the Mark-Houwink coefficients of this polymer in a widespread GPC eluent such as THF have never been determined. We provide in this contribution a simple relationship between the number-average molecular weight of poly(1,4-trans isoprene) determined by GPC in THF using polystyrene standards and its true value. 相似文献
97.
AnO(n logn) algorithm for planning a purely translational motion for a simple convex object amidst polygonal barriers in two-dimensional space is given. The algorithm is based on a new generalization of Voronoi diagrams (similar to that proposed by Chew and Drysdale [1] and by Fortune [2]), and adapts and uses a recent technique of Yap for the efficient construction of these diagrams.Work on this paper by the second author has been supported in part by a grant from the U.S.-Israeli Binational Science Foundation. 相似文献
98.
Sebastian Pfadler Micha Löffler Friedrich Dinkelacker Alfred Leipertz 《Experiments in fluids》2005,39(2):375-384
The turbulence and temperature field of Bunsen-type turbulent lean methane/air flames has been investigated using planar laser Rayleigh scattering (PLRS) and stereo particle image velocimetry (stereo PIV). Temporally averaged reaction progress variable plots have been computed from PLRS measurements in order to provide a basis with regards to the verification of computational fluid dynamics (CFD) models. Turbulence was characterised by stereo PIV in one plane for all three velocity components. Averaged velocity fields have been calculated, as well as Reynolds-decomposed fluctuation vector fields. Conditioned root mean square (RMS) values of the turbulent fluctuations in terms of unburnt and burnt gas could be determined by making use of the information gained from a threshold setting procedure in the PIV raw images. Furthermore, several length scales were measured indirectly from PIV vector plots. In this context, all integral length scales being accessible with stereo PIV were computed separately for the burnt and unburnt regions and were compared to each other. It could be observed that all integral length scales increased in the burnt zone. Additionally, the conditioned Taylor and Kolmogorov lengths have been extracted from the PIV field data, derived either from the zero-radius curvature of the correlation function or from common turbulence theory relations. 相似文献
99.
Interferences in the analysis of nanomolar concentrations of nitrate and phosphate in oceanic waters
This paper reports on investigations into interferences with the measurements of nanomolar nitrate + nitrite and soluble reactive phosphate (SRP) in oceanic surface seawater using a segmented continuous flow autoanalyser (SCFA) interfaced with a liquid-waveguide capillary flow-cell (LWCC). The interferences of silicate and arsenate with the analysis of SRP, the effect of sample filtration on the measurement of nanomolar nitrate + nitrite and SRP concentrations, and the stability of samples during storage are described.The investigation into the effect of arsenate (concentrations up to 100 nM) on phosphate analysis (concentrations up to 50 nM) indicated that the arsenate interference scaled linearly with phosphate concentrations, resulting in an overestimation of SRP concentrations of 4.6 ± 1.4% for an assumed arsenate concentration of 20 nM. The effect of added Si(OH)4 was to increase SRP signals by up to 36 ± 19 nM (at 100 μM Si(OH)4). However, at silicate concentrations below 1.5 μM, which are typically observed in oligotrophic surface ocean waters, the effect of silicate on the phosphate analysis was much smaller (≤0.78 ± 0.15 nM change in SRP). Since arsenate and silicate interferences vary between analytical approaches used for nanomolar SRP analysis, it is important that the interferences are systematically assessed in any newly developed analytical system.Filtration of surface seawater samples resulted in a decrease in concentration of 1.7-2.7 nM (±0.5 nM) SRP, and a small decrease in nitrate concentrations which was within the precision of the method (±0.6 nM). A stability study indicated that storage of very low concentration nutrient samples in the dark at 4 °C for less than 24 h resulted in no statistically significant changes in nutrient concentrations. Freezing unfiltered surface seawater samples from an oligotrophic ocean region resulted in a small but significant increase in the SRP concentration from 12.0 ± 1.3 nM (n = 3) to 14.7 ± 0.6 nM (n = 3) (Student's t-test; p = 0.021). The corresponding change in nitrate concentration was not significant (Student's t-test; p > 0.05). 相似文献
100.
A series of vanadium(V) complexes with unsymmetrical tridentate Schiff base ligands, obtained by the single condensation of R(−)-1,2-diaminopropane with salicylaldehyde and its derivatives, 2-hydroxy-1-naphthaldehyde, 2-hydroxyacetophenone, 1-hydroxy-2-acetonaphthone and 2-hydroxybenzophenone, were prepared. The complexes were characterized by elemental analysis and by their IR, CD, UV–Vis, 1D (1H, 51V) and 2D (COSY, NOESY, gHSQC) NMR spectra. Crystal structures of the mononuclear complex {R(−)-2-amino-1-N-[(2′-oxido-κO-4′,6′-dimethoxyphenyl)methylene]aminopropane-κ2N}dioxidovanadium(V), VO2(C12H17N2O3), 4, and of the dinuclear complex, di-μ-oxido-bis({R(−)-2-[1-(2-aminopropylimino)ethyl]-4-methylphenolato-κ3N,N′,O}oxidovanadium(V)), V2O4(C11H15N2O)2, 5, have been obtained by X-ray diffraction studies. The structure of 4 was revealed to be a distorted trigonal–bipyramidal coordination geometry, rarely encountered in VO2(tridentate Schiff base) complexes. Complexes 2 and 3 have the ability to catalyze the oxidation of prochiral sulfide substrates PhSR (R = Me, Bz) utilizing hydrogen peroxide or cumene hydroperoxide (CHPO) as the oxidant. 相似文献