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Simple Zeros of the Riemann Zeta-Function 总被引:1,自引:0,他引:1
Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26. 相似文献
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Quantum Zeno and anti-Zeno paradoxes 总被引:1,自引:0,他引:1
Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox).
We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure
change of state: an anti-Zeno paradox. 相似文献
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粉粒体两相流的电容层析成象测量 总被引:4,自引:0,他引:4
粉粒体系统中的固相浓度分布的在线测量是十分困难的问题.电容层析成象技术是一种近年来发展起来的非侵入式快速浓度场测量技术.它不干扰流场,不受流动中颗粒浓度、加速度、不透明等因素的制约.本文讨论其测量原理、应用、近期进展、存在的主要问题及其解决的对策. 相似文献
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ac Conductivity measurements are carried out across the metal to insulator transition in NiAl0.7Cr0.7Fe0.6O4. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling
behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency
conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime. 相似文献
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Eddy current-induced geometric distortions of single-shot, diffusion-weighted, echo-planar (DW-EP) images are a major confounding factor to the accurate determination of water diffusion parameters in diffusion tensor MRI (DT-MRI). Previously, it has been suggested that these geometric distortions can be removed from brain DW-EP images using affine transformations determined from phantom calibration experiments using iterative cross-correlation (ICC). Since this approach was first described, a number of image-based registration methods have become available that can also correct eddy current-induced distortions in DW-EP images. However, as yet no study has investigated whether separate eddy current calibration or image-based registration provides the most accurate way of removing these artefacts from DT-MRI data. Here we compare how ICC phantom calibration and affine FLIRT (http://www.fmrib.ox.ac.uk), a popular image-based multi-modal registration method that can correct both eddy current-induced distortions and bulk subject motion, perform when registering DW-EP images acquired with different slice thicknesses (2.8 and 5 mm) and b-values (1000 and 3000 s/mm(2)). With the use of consistency testing, it was found that ICC was a more robust algorithm for correcting eddy current-induced distortions than affine FLIRT, especially at high b-value and small slice thickness. In addition, principal component analysis demonstrated that the combination of ICC phantom calibration (to remove eddy current-induced distortions) with rigid body FLIRT (to remove bulk subject motion) provided a more accurate registration of DT-MRI data than that achieved by affine FLIRT. 相似文献
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Valdés Hernández Mdel C Gallacher PJ Bastin ME Royle NA Maniega SM Deary IJ Wardlaw JM 《Magnetic resonance imaging》2012,30(2):222-229
White matter loss, ventricular enlargement and white matter lesions are common findings on brain scans of older subjects. Accurate assessment of these different features is therefore essential for normal aging research. Recently, we developed a novel unsupervised classification method, named ‘Multispectral Coloring Modulation and Variance Identification’ (MCMxxxVI), that fuses two different structural magnetic resonance imaging (MRI) sequences in red/green color space and uses Minimum Variance Quantization (MVQ) as the clustering technique to segment different tissue types. Here we investigate how this method performs compared with several commonly used supervised image classifiers in segmenting normal-appearing white matter, white matter lesions and cerebrospinal fluid in the brains of 20 older subjects with a wide range of white matter lesion load and brain atrophy. The three tissue classes were segmented from T1-, T2-, T2?- and fluid attenuation inversion recovery (FLAIR)-weighted structural MRI data using MCMxxxVI and the four supervised multispectral classifiers available in the Analyze package, namely, Back-Propagated Neural Networks, Gaussian classifier, Nearest Neighbor and Parzen Windows. Bland–Altman analysis and Jaccard index values indicated that, in general, MCMxxxVI performed better than the supervised multispectral classifiers in identifying the three tissue classes, although final manual editing was still required to deliver radiologically acceptable results. These analyses show that MVQ, as implemented in MCMxxxVI, has the potential to provide quick and accurate white matter segmentations in the aging brain, although further methodological developments are still required to automate fully this technique. 相似文献
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DC magnetization, neutron depolarization and neutron diffraction (with both polarized and unpolarized neutrons) measurements
have been reported for the Co1.1−x
Zn
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Ge0.1Fe1.2O1 spinels with x=0.5, 0.6 and 0.7. Neutron depolarization and neutron diffraction measurements confirm the presence of a long range ferrimagnetic
ordering of the local canted spins in these ferrite samples. The observed features of low field magnetization have been explained
under the framework of thermally activated domain wall movement of ferrimagnetic arrangement of local canted spins. An important
role of magnetic anisotropy (due to the presence of Co2+ ions) in establishing the magnetic ordering and domain kinetics in these ferrites has been observed. 相似文献