Simple Zeros of the Riemann Zeta-Function

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.     

Quantum Zeno and anti-Zeno paradoxes

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.     

粉粒体两相流的电容层析成象测量

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．     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. 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.     

New insights into the transformation of calcium sulfate hemihydrate to gypsum using time-resolved cryogenic transmission electron microscopy

We use time-resolved cryogenic transmission electron microscopy (TR-cryo-TEM) on a supersaturated solution of calcium sulfate hemihydrate to examine the early stages of particle formation during the hydration of the hemihydrate. As hydration proceeds, we observe nanoscale amorphous clusters that evolve to amorphous particles and then reorganize to crystalline gypsum within tens of seconds. Our results indicate that a multistep particle formation model, where an amorphous phase forms first, followed by the transformation into a crystalline product, is applicable even at time scales of the order of tens of seconds for this system. The addition of a small amount of citric acid significantly delays the reorganization to gypsum crystals. We hypothesize that available calcium ions form complexes with the acid by binding to the carboxylic groups. Their incorporation into a growing particle produces disorder and extends the time over which the amorphous phase exists. We see evidence of patches of "trapped" amorphous phase within the growing gypsum crystals at time scales of the order of 24 h. This is confirmed by complementary X-ray diffraction experiments. Direct imaging of nanoscale samples by TR-cryo-TEM is a powerful technique for a fundamental understanding of crystallization and many other evolving systems.     

Shear free and blotless cryo-TEM imaging: a new method for probing early evolution of nanostructures

Cryogenic transmission electron microscopy (cryo-TEM) is a powerful method to image native state morphologies of nanoscale soft and hard objects suspended in solvents. Sample preparation is a critical step toward producing images at length and time scales of interest. We demonstrate a nearly shear-free sample thinning method which simultaneously allows imaging of evolving nanostructures at subsecond time scales. This device breaks the trade-off between high shear and short time scales typical in current cryo-TEM sample preparation methods. We demonstrate the low-shear feature of the new method by imaging wormlike micelles, showing an interconnected network, in contrast to the traditional sample preparation method which shows aligned micelles at similar time points. The time resolution of this method is demonstrated by imaging morphologies of calcium carbonate (formed through the reaction of calcium chloride with sodium carbonate) at subsecond time scales, capturing its evolution from an amorphous to a crystalline state. The impact of hyperbranched polyglycerol additives on the amorphous to crystalline transition in calcium carbonate at short times is examined. Early images at low shear provide unique fundamental insights into mechanisms of nanostructure evolution, thus offering a new paradigm for research in materials sciences, soft matter, and biological sciences.