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1.
2.
Given disjoint setsP
1,P
2, ...,P
d
inR
d
withn points in total, ahamsandwich cut is a hyperplane that simultaneously bisects theP
i
. We present algorithms for finding ham-sandwich cuts in every dimensiond>1. Whend=2, the algorithm is optimal, having complexityO(n). For dimensiond>2, the bound on the running time is proportional to the worst-case time needed for constructing a level in an arrangement
ofn hyperplanes in dimensiond−1. This, in turn, is related to the number ofk-sets inR
d−1
. With the current estimates, we get complexity close toO(n
3/2
) ford=3, roughlyO(n
8/3
) ford=4, andO(n
d−1−a(d)
) for somea(d)>0 (going to zero asd increases) for largerd. We also give a linear-time algorithm for ham-sandwich cuts inR
3 when the three sets are suitably separated.
A preliminary version of the results of this paper appeared in [16] and [17]. Part of this research by J. Matoušek was done
while he was visiting the School of Mathematics, Georgia Institute of Technology, Atlanta, and part of his work on this paper
was supported by a Humboldt Research Fellowship. W. Steiger expresses gratitude to the NSF DIMACS Center at Rutgers, and his
research was supported in part by NSF Grants CCR-8902522 and CCR-9111491. 相似文献
3.
Rolf Dittmann Heinz-Jürgen Feld Wolfgang Samenfink Sigmar Wittig 《Particle & Particle Systems Characterization》1994,11(5):379-384
In utilizing the advantages of extinction measurements in micron and especially submicron particle characterization, the properties of a multiple wavelength extinction technique have been the subject of extended theoretical studies. Furthermore, an experimental set-up was designed which provides high flexibility owing to its modular design. The performance of the technique described is demonstrated by a large variety of applications in aerosol and combustion research and in large-scale industrial systems. It was found to be a reliable tool in characterizing dense particulate systems. 相似文献
4.
Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain
and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general
spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary
plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these
polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit
a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit
Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid
dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL
condition even in the presence of viscous fluxes. 相似文献
5.
6.
Michael Höft Jochen Weinzierl Rolf Judaschke 《International Journal of Infrared and Millimeter Waves》2002,23(7):1127-1146
Holography is a promising technique for power combining applications in the frequency range of short millimeter and submillimeter waves. In this paper, quasi-optical holographic power combining circuits are investigated. An equivalent network is utilized which rigorously models horn arrays and biperiodic dielectric structures in order to design computer-generated holograms. We apply the network model to a 5-element quasi-optical power combiner and demonstrate its capability. The hologram is designed for 150 GHz and has an efficiency of 92.5 % with a 90 % bandwidth of 5.3 %. With the aid of a broadband waveguide power divider and a vector field measurement system, the circuit is analyzed. 相似文献
7.
We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W?1, p spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain Lp estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
8.
9.
10.
Rolf Vonhoff 《Mathematische Nachrichten》1998,193(1):199-210
In the paper, a new method of constructing asymptotic solutions of differential equations on manifolds with singularities is presented. This method allows not only to widen essentially the space of asymptotics but also to obtain explicit formulas for asymptotic expansions, in particular, in the case when in a neighborhood of a singular point there exist strata of different dimensions. 相似文献