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.     

Practical implications of ionic strength effects on particle retention in thermal field-flow fractionation

Modification of ionic strength of an aqueous or non-aqueous carrier solution can have profound effects on the particle retention behavior in thermal field-flow fractionation (ThFFF). These effects can be considered as either advantageous or not depending on the performance criteria under consideration. Aside from the general increase in retention time of particulate material (latexes and silica particles), our experiments indicate improvement in resolution with increases in electrolyte concentration. Absence of an electrolyte in the carrier solution causes deviations from the theoretically expected linear behavior between the retention parameter lambda (a measure of the extent of interaction between the applied field and the particle) and the reciprocal temperature drop across the channel walls. A negative interaction parameter delta(w), of about -0.170 was determined for 0.105- and 0.220-microm polystyrene (PS) latex particles suspended in either a 0.25 or a 1.0 mM TBAP-containing acetonitrile carrier and for 0.220 microm PS in 0.50 and 1.0 mM NaCl-containing aqueous medium. This work also demonstrates that optimum electrolyte concentrations can be chosen to achieve reasonable experimental run-times, good resolution separations, and shifts in the steric inversion points at lower field strengths, and that too high electrolyte concentrations can have deleterious effects such as band broadening and sample loss through adsorption to the channel accumulation surface. The advantages of using ionic strength rather than field strength to effect desired changes are lowered power consumption and possible application of ThFFF to high temperature-labile samples.     

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.     

Local canted spin behaviour in Co1.4−x Zn x Ge0.4Fe1.2O4 spinels: A macroscopic, mesoscopic and microscopic study

DC magnetization, neutron depolarization and neutron diffraction (with both polarized and unpolarized neutrons) measurements have been reported for the Co_1.1−x Zn _x Ge_0.1Fe_1.2O₁ 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.     

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.