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31.
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
32.
V. M. Baev J. Eschner E. Paeth R. Schüler P. E. Toschek 《Applied physics. B, Lasers and optics》1992,55(6):463-477
A multi-mode diode laser with an external cavity is studied experimentally and theoretically for its application to intra-cavity spectroscopy. One facet of a typical Ga0.89Al0.11As laser diode was antireflection-coated by deposition of HfO2 such that 10–3 residual reflectivity was left over. This diode was placed in an external optical cavity. The emission spectrum of this diode laser is highly sensitive to any frequency-dependent loss in the cavity, and the detectivity of such a loss grows with the pump rate. Even close to threshold, the absorption at 780 nm of Rb atoms with a density of 5×1010 cm–3 has been detected. An adequate model for diode lasers based on rate equations and including frequency-dependent gain saturation is developed and applied to the calculations of output spectra. The sensitivity of these spectra to intra-cavity absorption is determined by the overall cavity loss — which is rather high — and the fraction of spontaneous emission in the total emission, in contrast with dye lasers where it is limited by nonlinear mode coupling. Various criteria for the sensitivity are suggested. The smallest detectable absorption with a perfectly antireflection-coated laser is 10–6 cm–1. Improvement of the characteristics of the laser diode would increase the sensitivity. 相似文献
33.
34.
Andreas Rößler 《BIT Numerical Mathematics》2006,46(1):97-110
A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance. 相似文献
35.
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
36.
Andreas Rößler 《BIT Numerical Mathematics》2007,47(3):657-680
The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main
novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due
to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with
order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly.
AMS subject classification (2000) 65C30, 65L06, 60H35, 60H10 相似文献
37.
Peptidosulfonamides are an emerging group of peptidomimetics with a variety of applications in medicinal chemistry. We present a novel approach to the synthesis of peptidosulfonamides, and apply it to a series of new potential inhibitors of the bacterial peptidoglycan biosynthesis enzymes MurD and MurE. The synthesis was conducted via N-phthalimido β-aminoethanesulfonyl chlorides, which are new building blocks for the synthesis of peptidosulfonamides. In the most crucial step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of either SOCl2 or SOCl2/DMF, and then coupled to the C-protected amino acid. None of the compounds significantly inhibited MurD, however, some inhibited MurE; one had an IC50 below 200 μM, which constitutes a promising starting point for further development. Molecular modelling simulations were performed on two analogues to investigate the absence of inhibitory activity of the sulfonamide compounds on MurD. 相似文献
38.
39.
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
40.
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