Hilbert-Speiser number fields for a prime p inside the p-cyclotomic field

Let p be a prime number. We say that a number field F satisfies the condition when for any cyclic extension N/F of degree p, the ring of p-integers of N has a normal integral basis over . It is known that F=Q satisfies for any p. It is also known that when p?19, any subfield F of Q(ζp) satisfies . In this paper, we prove that when p?23, an imaginary subfield F of Q(ζp) satisfies if and only if and p=43, 67 or 163 (under GRH). For a real subfield F of Q(ζp) with F≠Q, we give a corresponding but weaker assertion to the effect that it quite rarely satisfies .     

Simultaneous determination of ginsenoside Rg1, Re and notoginsenoside R1 in human plasma by LC‐MS/MS and its application in a pharmacokinetic study in Chinese volunteers

A rapid and sensitive liquid chromatography–tandem mass spectrometry (LC‐MS/MS) method has been developed and validated for simultaneous quantification of ginsenosides Rg₁, Re and notoginsenoside R₁ in human plasma. Chromatography was performed on Capcell Pak C₁₈ MG II column using a binary gradient using mobile phase A (5 mm ammonium formate solution) and B (methanol, containing 5 mm ammonium formate) at a flow rate of 0.3 mL/min. The entire chromatographic run time was 3.2 min. Quantification was achieved using multiple reaction monitoring in positive mode using API 3000. This method was validated in terms of specificity, linearity, precision, accuracy, matrix effect and stability. The calibration curves were linear in the concentration range of 0.020–5.00 ng/mL for ginsenosides Rg₁, Re and notoginsenoside R₁. The lower limit of quantification (LLOQ) of this method was 0.020 ng/mL. The intra‐run and inter‐run precision values were within 12.31% for ginsenoside Rg₁, 14.13% for ginsenoside Re and 11.46% for notoginsenoside R₁ at their LLOQ levels. The samples were stable under all tested conditions. This method was successfully applied to study the pharmacokinetics of ginsenoside Rg₁ and notoginsenoside R₁ in 24 healthy volunteers following oral administration of 200 mg Sanqi Tongshu Enteric‐Pellets Capsule.     

Paschen curve approach to investigate electron density and deposition rate of Cu in magnetron sputtering system

In this work, Paschen curve for argon gas was obtained during copper deposition using a DC magnetron sputtering system. Five process parameters of Paschen curve were used to obtain the electron density and deposition rate of the deposited nanostructured thin films. Plasma parameter such as electron density was correlated with the deposition rate. It is observed that a minimum deposition rate was obtained for the plasma process parameter corresponding to the Paschen minimum. This investigation helps to understand and optimize the quality of nanostructured thin films depending on the process parameters.     

Parameters Affecting Heat Transfer During Condensation Inside Micropipes: Surface Tension Effect. Paper II

Experimental and analytical investigation was carried out to show the effect of surface tension on the heat transfer coefficient of gas flow inside micropipe heat exchangers during the condensation process. An empirical correlation was formulated for the coefficient of the convective heat transfer. A comprehensive comparison between the experimental results with published correlations in the literature and that obtained by the developed correlation was conducted. The results showed that the predicted heat transfer coefficient of the proposed correlation was closer to the experimental results than any other correlation, a finding related to the consideration of the surface tension.     

Weighing Neutrinos in f(R) Gravity in Light of BICEP2

We constrain the neutrino mass in f(R) gravity using the latest observations from the Planck, BAO and BICEP2 data. We find that the measurement on the B-modes can break the degeneracy between the massive neutrinos and the f(R) gravity. We find a non-zero value of the Compton wavelengths B0 at a 68% confidence level for the f(R) model in the presence of massive neutrinos when the BICEP2 data is used. Furthermore, the tension on the tensor-to-scalar ratios between the measured values from Plank and BICEP2 is significantly reconciled in our model.     

Frequency and voltage dependence of dielectric properties and electric modulus in Au/PVC + TCNQ/p-Si structure at room temperature

Au/PVC + TCNQ/p-Si structure was fabricated and real and imaginary parts of the dielectric constant (ɛ′, ɛ″), loss tangent (tanδ), and the real and imaginary parts of the electric modulus (M′, M″) and ac conductivity (σ_ac) of this structure have been investigated in wide frequency a range of 1 kHz–5 MHz at room temperature. All of these parameters were found strong function of frequency and voltage especially in the inversion and depletion regions at low frequencies due to interfacial polarization and charges at interface states (N_ss). The decrease in ɛ′ and ɛ″ with increasing frequency indicated that the interfacial dipoles have less time to orient themselves in the direction of the alternate field. While the value of M′ increase with increasing frequency and reach a maximum, M″ shows a peak and the peak position shifts to higher frequency with increasing applied voltage. The ln(σ_ac) vs ln(ω) plot of the structure for 0.5 V has three linear regions (I, II and III) with different slopes which correspond to low, intermediate and high frequency ranges, respectively. Such behavior of ln(σ_ac) vs ln(ω) plot indicated that there are three different conduction mechanisms in the Au/PVC + TCNQ/p-Si structure at room temperature.     

SL(2,R)上的Fourier变换的渐近性质的注记

该文借助于犛犔（２，犚）上李代数及其万有包络代数讨论了犛犔（２，犚）上函数的Ｆｏｕｒｉｅｒ变换在无穷远处下降的阶与函数的光滑性的关系，我们得到的结论较［６］中的结论好，并由此得到犆２犮（犌）中的Ｐｌａｎｃｈｅｒｅｌ定理．