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41.
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
42.
43.
V. V. Panić A. B. Dekanski S. K. Milonjić V. B. Mišković-Stanković B. Ž. Nikolić 《Russian Journal of Electrochemistry》2006,42(10):1055-1060
Electrocatalytic properties of RuO2/Ti anode with different coating masses, which are prepared by the alkoxide sol-gel procedure, are investigated in chlorine
and oxygen evolution reactions by polarization measurements and electrochemical impedance spectroscopy in H2SO4 and NaCl electrolytes. According to polarization measurements, the activity of anodes at overpotentials below 100 mV is independent
of coating mass. However, impedance measurements above 100 mV reveal changes in the activity of anodes in chlorine evolution
reaction for different coating masses. The diffusion limitations related to the evolved chlorine are registered in low-frequency
domain at 1.10 V (SCE), diminishing with the increase in potential to the 1.15 V (SCE). The observed impedance behavior is
discussed with respect to the activity model for activated titanium anodes in chlorine evolution reaction involving formation
of gas channels within porous coating structure. Gas channels enhance the mass transfer rate similarly to the forced convection,
which also increases the activity of anode. This is more pronounced for the anode of greater coating mass due to its more
compact surface structure. The more compact structure appears to be beneficial for gas channels formation.
Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1173–1179.
The text was submitted by the authors in English. 相似文献
44.
G. Bilalbegović 《Zeitschrift für Physik B Condensed Matter》1987,69(1):117-120
The interfacial tension of a three-dimensional Ising model in the whole temperature region is calculated by the real-space renormalisation group methods. The cumulant and the finite-cluster approximations with different projection rules are used. The results are consistent with expected low-temperature and global behaviour of the interfacial tension in the three-dimensional model. 相似文献
45.
The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact,
simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and
a few logarithms, all of very simple arguments.
Received: 31 January 2002 / Published online: 26 April 2002 相似文献
46.
K. Prokeš 《Czechoslovak Journal of Physics》2002,52(2):253-258
Many materials exhibit various magnetic phenomena as a function of magnetic field, temperature and/or pressure. Usually, bulk magnetic measurements provide first information on the magnetic state of the material by measuring their response on the applied magnetic field. However, it is necessary to investigate materials also on a microscopic scale. This is often done by means of neutron scattering. In this contribution we discuss basic ideas of this method and we report on few experimental results obtained with a split-pair coil 14.5 T superconducting magnet which can be combined with dilution stick offering temperatures as low as 30 mK and/or with a small clamped-type pressure cell which offers pressure up to 1.0 GPa. 相似文献
47.
Dragomir Ž. Đoković 《Combinatorica》1994,14(3):375-377
No Hadamard matrices of order 956 appear in the literature. In this note we construct two such matrices. They are both of Goethals-Seidel type. As a consequence of this and of a result of Seberry and Yamada, we conclude that there exist 4-Williamson type matrices of order 1913.This work was supported by NSERC of Canada Grants A-5285 and EQP0107539. 相似文献
48.
49.
We have investigated the structure of spider dragline silk by X-ray diffraction over a broad temperature range from room temperature
up to thermal denaturation conditions. The dominating signal from the β-sheet crystallites is analyzed. Pronounced changes
of scattering intensity starting at temperatures around 150 °C are observed. These changes are discussed in view of the respective
lattice constants, crystal size, size distribution, crystallite number density and amino acid composition.
PACS 87.68.+z; 87.15.-v; 87.64.Bx 相似文献
50.