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.     

Integration matrix based on arbitrary grids with a preconditioner for pseudospectral method

A matrix representation of integration for arbitrary grids is introduced. Suitable results are then obtained to be used along with differentiation matrix preconditioner to implement Pseudospectral method on integro-differential equations using arbitrary grids. Numerical examples are given to clarify the efficiency of the new method.     

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.     

Simultaneous sensing of L-tyrosine and epinephrine using a glassy carbon electrode modified with nafion and CeO2 nanoparticles

An electrochemical sensor was developed and tested for detection of L-tyrosine in the presence of epinephrine by surface modification of a glassy carbon electrode (GCE) with Nafion and cerium dioxide nanoparticles. Fabrication parameters of a surfactant-assisted precipitation method were optimized to produce 2–3 nm CeO₂ nanoparticles with very high surface-to-volume ratio. The resulting nanocrystals were characterized structurally and morphologically by X-ray diffractometery (XRD), scanning and high resolution transmission electron microscopy (SEM and HR-TEM). The nanopowder is sonochemically dispersed in a Nafion solution which is then used to modify the surface of a GCE electrode. The electrochemical activity of L-tyrosine and epinephrine was investigated using both a Nafion-CeO₂ coated and a bare GCE. The modified electrode exhibits a significant electrochemical oxidation effect of L-tyrosine in a 0.2 M Britton-Robinson (B-R) buffer solution of pH 2. The electro-oxidation peak current increases linearly with the L-tyrosine concentration in the molar concentration range of 2 to 160 μM. By employing differential pulse voltammetry (DPV) for simultaneous measurements, we detected two reproducible peaks for L-tyrosine and epinephrine in the same solution with a peak separation of about 443 mV. The detection limit of the sensor (signal to noise ratio of 3) for L-tyrosine is ~90 nM and the sensitivity is 0.20 μA μM⁻¹, while for epinephrine these values are ~60 nM and 0.19 μA μM⁻¹. The sensor exhibited excellent selectivity, sensitivity, reproducibility and stability as well as a very good recovery time in real human blood serum samples.

Simultaneous electrochemical determination of L-tyrosine and epinephrine in blood plasma with Nafion-CeO₂/GCE modified electrode showing a 443 mV peak-to-peak potential difference between species oxidation peak currents.

     

Green synthesis of silver and gold nanoparticles using Rosa damascena and its primary application in electrochemistry

Biosynthesis and characterizations of nanoparticles have become an important branch of nanotechnology. In this paper, green synthesis of gold nanoparticles (AuNPs) and silver nanoparticles (AgNPs) using the flower extract of Rosa damascena as a reducing and stabilizing agent, has been discussed. This approach is simple, cost-effective and stable for a long time, reproducible at room temperature and in an eco-friendly manner to obtain a self-assembly of AuNPs and AgNPs. The resulting nanoparticles are characterized using UV–vis, TEM, XRD and FT-IR spectroscopic techniques. A modified glassy carbon electrode using AuNPs (AuNPs/GCE) was investigated by means of cyclic voltammetry in a solution of 0.1 M KCl and 5.0×10⁻³ M [Fe(CN)₆]^3−/4−. The results show that electronic transmission rate between the modified electrode and [Fe(CN)₆]^3−/4− increased.     

Selective Voltammetric Determination of Tartrazine in the Presence of Red 10B by Nanogold‐modified Carbon Paste Electrode

A nanogold modified carbon paste electrode (NG‐CPE) was fabricated and used as selective voltammetric sensor for determination of Tartrazine in the presence of Red 10B using cyclic voltammetry (CV), differential pulse voltammetry (DPV), and chronoamperometry (CHA). Electrochemical parameters including the diffusion coefficient (D), the electron transfer coefficient (aXXXXX), and the electron transfer number (n) were determined for the oxidation of Tartrazine. This modified electrode can be applied to simultaneous determination of Tartrazine and Red 10B, because of considerable decreases of anodic overpotentials for both compounds. After optimizing the experimental conditions, the anodic peak current of Tartrazine was linear to its concentration in the range of 0.05‐1.5 μmol l^?1, and the detection limit was 0.017 μmol l^?1 in phosphate buffer solution (PBS) at pH 4.0. The modified electrode has good stability and repeatability. It was applied to the determination of Tartrazine and Red 10B in soft drinks with satisfactory results.     

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.