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21.
Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities.
The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria.
This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an
interaction proportional to r
b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the
3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief
of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some
hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial
framework. 相似文献
22.
Fengfu Fu Liangjun Xu Wei Ye Yiquan Chen Mingyu Jiang Xueqin Xu 《中国颗粒学报》2006,4(6):323-326
Different-sized aerosols were collected by an Andersen air sampler to observe the detailed morphology of the black carbon (BC) aerosols which were separated chemically from the other accompanying aerosols, using a Scanning Electron Microscope equipped with an Energy Dispersive X-ray Spectrometer (SEM-EDX). The results indicate that most BC aerosols are spherical particles of about 50 nm in diameter and with a homogeneous surface. Results also show that these particles aggregate with other aerosols or with themselves to form larger agglomerates in the micrometer range. The shape of these 50-nm BC spherical particles was found to be very similar to that of BC particles released from petroleum-powered vehicular internal combustion engines. These spherical BC particles were shown to be different from the previously reported fullerenes found using Matrix-Assisted Laser Desorption/Ionization Time-Of-Flight Mass Spectrometry (MALDI-TOF-MS). 相似文献
23.
养殖池塘沉积物的重金属分布及污染特征 总被引:3,自引:0,他引:3
浙江省淅西北地区淡水养殖池塘沉积物重金属调查研究表明,养殖池塘沉积物中7种重金属元素分布不均衡,差异也较大,除Hg和Cr元素外,其余重金属元素已大大超过土壤本底值.虽然其实测含量都未超出国家规定的标准值范围,但沉积物中重金属元素对养殖水环境、养殖品种存在的潜在污染与危害值得关注.污染指数评价显示,养殖池塘沉积物中主要污染物质为Cu和Cr,而Hg、Pb污染程度相对较轻. 相似文献
24.
Because of package, a single FBG has dual Bragg wavelength. One is sensitive to stress and the other is sensitive to temperature. By using the special mechanism, the wavelengths can be tuned by stress and temperature respectively. 相似文献
25.
A new constant-pressure molecular dynamics (MD) method is developed to simulate the dynamic behavior and structure transition of finite system under external pressure. In this method, no artificial parameter is introduced and the computation overheads are very small. As an application, a hard-soft transition of single wall carbon nanotube (SWCNT) under external pressure is found, which is in agreement with the experiments.
相似文献26.
5‐Methylene‐2‐oxazolidinone (1) and 5‐methylene‐1,3‐thiazolidine‐2‐thione (4) react with various isocyanates to give the corresponding urethanes 3 and 5 in high yields in the presence of palladium(0) or palladium(II) catalyst under mild reaction conditions. A mechanism is proposed. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
27.
Hyun Chul Choi Min Kyu Lee Hyun Joon Shin Seung Bin Kim 《Journal of Electron Spectroscopy and Related Phenomena》2003,130(1-3):85-96
To investigate the formation of a solid electrolyte interface (SEI) on the Li1+xV3O8 electrode surface in the thermodynamic stability range of the organic electrolyte, we applied scanning photoelectron microscopy (SPEM) to a pristine electrode and to an electrode after ten cycles. The F K-edge absorption spectrum of the cycled electrode showed that LiF forms on the electrode surface during the lithium insertion–extraction process in the Li1+xV3O8/Li cell. The photoelectron spectrum for the cycled electrode showed intense spectral features corresponding to Li 1s, F 2s, F 2p, and P 2p electron signals, whereas these spectral features were of negligible intensity for the pristine electrode. The above results give strong support for the formation of an SEI that consists of LiF and compounds containing phosphorus during operation of the battery. The SPEM images also revealed that the fluorine distribution on the surface of the cycled electrode was inhomogeneous. 相似文献
28.
The growth mechanism of the peritectic η phase involving the peritectic reaction and peritectic transformation in Cu-70%Sn alloy was investigated under directional
solidification. The results show that a major growth mechanism in thickening of the peritectic η-layer is not the peritectic reaction but the peritectic transformation. The transformation temperature and isothermal time
play crucial roles in determining the volume fraction and the thickness of the peritectic η phase. With the increase of the temperature and isothermal time, the volume fraction of the peritectic η phase increases. The regressed data show that the relationship between the thickness of η phase (Δx) and the transformation temperature (T) meets the following equation In Δx=6.5−1673 1 / T. Additionally, there exists a relationship between the thickness of the η phase (Δx) and the isothermal time (t) at the 9 mm solidification distance below the peritectic reaction interface, Δx=0.72t
1/2, which is consistent with the theoretical model.
Supported by the National Science Foundation of China (Grant No. 50395102) 相似文献
29.
Yong Joon Park Min Gyu KimYoung-Sik Hong Xianglan WuKwang Sun Ryu Soon Ho Chang 《Solid State Communications》2003,127(7):509-514
Li[NixLi(1/3−2x/3)Mn(2/3−x/3)]O2 (X=0.17, 0.25, 0.33, 0.5) compounds are prepared by a simple combustion method. The Rietvelt analysis shows that these compounds could be classified as having the α-NaFeO2 structure. The initial charge-discharge and irreversible capacity increases with the decrease of x in Li[NixLi(1/3−2x/3)Mn(2/3−x/3)]O2. Indeed, Li[Ni0.50Mn0.50]O2 compound shows relatively low initial discharge capacity of 200 mAh/g and large capacity loss during cycling, with Li[Ni0.17Li0.22Mn0.61]O2 and Li[Ni0.25Li0.17Mn0.58]O2 compounds exhibit high initial discharge capacity over 245 mAh/g and stable cycle performance in the voltage range of 4.8 -2.0 V. On the other hand, XANES analysis shows that the oxidation state of Ni ion reversibly changes between Ni2+ and about Ni3+, while the oxidation state of Mn ion sustains Mn4+ during charge-discharge process. This result does not agree with the previously reported ‘electrochemistry model’ of Li[NixLi(1/3−2x/3)Mn(2/3−x/3)]O2, in which Ni ion changes between Ni2+ and NI4+. Based on these results, we modified oxidation-state change of Mn and Ni ion during charge-discharge process. 相似文献
30.
本文给出递归集的Hausdorff维数的下界估计,并由此确定了一类递归集的维数,所获结果包含并推广了Bedford,Dekking及文志英、钟红柳等人的有关结果。 相似文献