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111.
In the late 1950s, B. Segre introduced the fundamental
notion of arcs and complete arcs [48,49]. An arc in a nite
projective plane is a set of points with no three on a line and
it is complete if cannot be extended without violating this
property. Given a projective plane
, determining
, the size of its
smallest complete arc, has been a major open question in finite
geometry for several decades. Assume that
has order
q, it was shown by Lunelli
and Sce [41], more than 40 years ago, that
. Apart from this bound,
practically nothing was known about
, except for the case
is the Galois plane. For
this case, the best upper bound, prior to this paper, was
O(q
3/4)
obtained by Sznyi using the properties of the Galois field
GF(q).In this paper, we prove that
for any projective plane
of order
q, where
c is a universal constant.
Together with Lunelli-Sces lower bound, our result determines
up to a polylogarithmic
factor. Our proof uses a probabilistic method known as the
dynamic random construction or Rödls nibble. The proof also
gives a quick randomized algorithm which produces a small
complete arc with high probability.The key ingredient of our proof is a new concentration
result, which applies for non-Lipschitz functions and is of
independent interest.* Research supported in part by grant RB091G-VU from
UCSD, by NSF grant DMS-0200357 and by an A. Sloan
fellowship.Part of this work was done at AT&T Bell Labs and
Microsoft Research 相似文献
112.
Nguyen H. V. Hu'ng Tran Ngoc Nam 《Transactions of the American Mathematical Society》2001,353(12):5029-5040
Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.
113.
Tran Duc Thiep Truong Thi An Nguyen The Vinh Phan Viet Cuong A. G. Belov O. D. Maslov Trinh Thi Thu My 《Physics of Particles and Nuclei Letters》2007,4(5):397-402
We have carried out the study on the isomeric ratios in (γ,p) photonuclear reactions with isotopes
40
92
Zr and
74
183
W in the giant dipole resonance (GDR) region. The targets were irradiated with bremsstrahlungs produced by electron accelerator
Microtron MT-25 of the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia. Spectra
of the irradiated samples were measured with a spectroscopic system consisting of 8192-channel analyzer CANBERRA and high-energy
resolution semiconductor detector CANBERRA. The results were discussed and compared with those of other authors.
The text was submitted by the authors in English. 相似文献
114.
We report a direct observation of the temperature field on a steel specimen during ablation by multiple femtosecond laser pulses using an infrared thermography technique. From the experimental results and simulation study of the temperature field, we quantified the deposited thermal power into the specimen during the ablation process. We found that more than two thirds of the incident laser power was deposited in the steel specimen when ablated by multiple femtosecond laser pulses. This result provides further understanding of the heating effect in materials processing by ultrashort laser pulses. 相似文献
115.
H. Tran V. Dana X. Thomas 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,108(3):342-362
Line intensities are measured for 546 transitions belonging to 13 bands of the main isotopologue 12C2H2 of the acetylene molecule, in the 1.5-μm spectral domain. A multispectrum fitting procedure is used to retrieve line parameters from Fourier transform spectra. Prior to this work, line intensities were known for only 4 bands in this spectral region, from the work of El Hachtouki and Vander Auwera [Absolute line intensities in acetylene: the 1.5 μm region. J Mol Spectrosc 2002;216:355-62]. An excellent agreement is found with the results of these authors, showing that the accuracy of both results is likely better than 1% for the strong bands. However, the spectrum becomes very crowded when one wants to study weaker bands, so that the average accuracy of the intensities reported in the present work is 5%. From these data, vibrational transition dipole moments squared and Herman-Wallis coefficients have been determined for all the bands. 相似文献
116.
L.H. Nguyen T.V. Phi P.Q. Phan H.N. Vu C. Nguyen-Duc F. Fossard 《Physica E: Low-dimensional Systems and Nanostructures》2007,37(1-2):54
It has been recently demonstrated that carbon nanotubes (CNTs) represent a new type of chemical sensor capable of detecting a small concentration of molecules such as CO, NO2, NH3.In this work, CNTs were synthesized by chemical vapor deposition (CVD) on the SiO2/Si substrate by decomposition of acetylene (C2H2) on sputtered Ni catalyst nanoparticles. Their structural properties are studied by atomic force microscopy, high-resolution scanning electron microscopy (HRSEM) and Raman spectroscopy. The CNTs grown at 700 °C exhibit a low dispersion in size, are about 1 μm long and their average diameter varies in the range 25–60 nm as a function of the deposition time. We have shown that their diameter can be reduced either by annealing in oxygen environment or by growing at lower temperature (less than 600 °C).We developed a test device with interdigital Pt electrodes on an Al2O3 substrate in order to evaluate the CNTs-based gas sensor capabilities. We performed room temperature current–voltage measurements for various gas concentrations. The CNT films are found to exhibit a fast response and a high sensitivity to NH3 gas. 相似文献
117.
H. Isnard M. Granet C. Caussignac E. Ducarme A. Nonell B. Tran F. Chartier 《Spectrochimica Acta Part B: Atomic Spectroscopy》2009,64(11-12):1280-1286
In the nuclear domain, precise and accurate isotopic composition determination of elements in spent nuclear fuels is mandatory to validate neutron calculation codes and for nuclear waste disposal. The present study presents the results obtained on Cs isotope ratio by mass spectrometric measurements. Natural cesium is monoisotopic (133Cs) whereas cesium in spent fuels has 4 isotopes (133Cs, 134Cs, 135Cs, and 137Cs). As no standard reference material is available to evaluate the accuracy of Cs isotopic measurements, a comparison of cesium isotopic composition in spent nuclear fuels has been performed between Thermal Ionization Mass Spectrometry (TIMS) and a new method involving Multiple Collector Inductively Coupled Plasma Mass Spectrometry (MC-ICPMS) measurements. For TIMS measurements, isotopic fractionation has been evaluated by studying the behavior of cesium isotope ratios (133Cs/137Cs and 135Cs/137Cs) during the analyses. For MC-ICPMS measurements, the mass bias effects have been corrected with an external mass bias correction using elements (Eu and Sb) close to cesium masses. The results obtained by the two techniques show good agreement: relative difference on 133Cs/137Cs and 135Cs/137Cs ratios for two nuclear samples, analyzed after chemical separation, ranges from 0.2% to 0.5% depending on the choice of reference value for mass bias correction by MC-ICPMS. Finally the quantification of the 135Cs/238U ratio by the isotope dilution technique is presented in the case of a MOx (mixed oxide) spent fuel sample. Evaluation of the global uncertainties shows that this ratio could be defined at an uncertainty of 0.5% (k = 2). The intercomparison between two independent mass spectrometric techniques is fundamental for the evaluation of uncertainty when no isotopic standard is available. 相似文献
118.
119.
Breakdown conditions for creation of the hollow cathode discharge in the nozzle passed through the rf powered electrode and creation of the plasma jet channel in PCVD reactor are studied. Pure nitrogen is used for measurements. The creation of jet channel is easier for smaller rf electrodes. The breakdown depends on the pressure and on the gas inflow rate. The plasma potential and the self-bias potential is influenced by the covering of reactor walls and the rf electrode by a dielectric layer. 相似文献
120.