Perturbations of Single-field Inflation in Modified Gravity Theory

In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form $f(R)$. Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so in despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure $f(R)$ theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there are large parameter space in these models, we show that it is easy to fit the data very well.Comment: 9 pages, 1 figure, substantially improved, matching with the published versio

Socioeconomic Study on Farmers’ Adoption of Integrated Pest Management (IPM) Strategies in Brassica Vegetable Crops in China

Crop Production/Industries,

Elegant design of carbon nanotube foams with double continuous structure for metamaterials in a broad frequency range

Carbon nanotube (CNT) foams with negative permittivity and permeability are successfully prepared by chemical vapor deposition (CVD) and post-treatment. A double negative metamaterial in the 1-1000 MHz frequency range with double continuous structure results by effectively compounding the CNT foam with a polymer material, i.e. epoxy or nanosilver silicone resin. The negative permeability is specifically attributed to the three-dimensional CNT interactions as clear from the study of the relation of the material microstructure and the macroscopic measurements. Compared to CNT foam/epoxy composites, CNT foam/nanosilver/silicone composites have a lower permeability but a more excellent electrical conductivity or permittivity. It is also shown that the carbon source time during CVD and post-pressurization can be adjusted to allow for both negative permittivity and permeability. This contribution highlights a convenient method to obtain a metamaterial in a much larger frequency range (ca. 1 to 1000 MHz) than the state-of-the-art. It thus supports the expansion of the application range of metamaterials and simplifies their preparation, which is of great significance for the wider use of these materials

Preparation and electrochemical performance of hollow activated carbon fiber self-supported electrode for supercapacitor

Hollow activated carbon fiber (HACF) with high specific surface area and high charge storage capability was prepared by pre-oxidation, carbonization and KOH-activation from polyacrylonitrile (PAN). HACF was used as self-supported working electrode directly without any binder and conductive agent. The effect of the activation time on specific surface area of HACF was studied intensively. The results show that the specific surface area of HACF increased with the increase of activation time from 0.5 h to 1.5 h, and then decreased with further increase of activation time. Highest specific surface area of 1873 m(2)g(-1) and micropore volume of 0.61 cm(3)g(-1) were obtained in HACF activated for 1.5 h. Electrochemical properties of HACF can be improved with increase of activation time, but excessive activation results in the decrease of specific surface area and increase of internal resistance of HACF. The self-supported electrode of HACF possesses a large specific capacitance of 323 F g(-1) at 0.05 A g(-1) and 216 F g(-1) at 1 A g(-1). Therefore, HACF can be a promising self-supported electrode for high performance supercapacitors

The Cost of Obeying the Law?: The Seventh Circuit Rejects the Bona Fide Error Defense from a Debt Collector Who Followed the Then-Binding Law

It is expected that people should follow the law, which includes the statutes themselves and the judicial rulings interpreting those statutes. However, if the binding judicial interpretation changes, should the parties be liable for their behavior following the old binding judicial interpretation of a federal statute at the time when it was still in effect? Or, should there be any defense that would allow the parties to shield themselves from liability for a good-faith reliance on the old binding judicial interpretation

Periodic Radio Variability in NRAO 530: Phase Dispersion Minimization Analysis

In this paper, a periodicity analysis of the radio light curves of the blazar NRAO 530 at 14.5, 8.0, and 4.8 GHz is presented employing an improved Phase Dispersion Minimization (PDM) technique. The result, which shows two persistent periodic components of $\sim 6$ and $\sim 10$ years at all three frequencies, is consistent with the results obtained with the Lomb-Scargle periodogram and weighted wavelet Z-transform algorithms. The reliability of the derived periodicities is confirmed by the Monte Carlo numerical simulations which show a high statistical confidence. (Quasi-)Periodic fluctuations of the radio luminosity of NRAO 530 might be associated with the oscillations of the accretion disk triggered by hydrodynamic instabilities of the accreted flow. \keywords{methods: statistical -- galaxies: active -- galaxies: quasar: individual: NRAO 530}Comment: 8 pages, 5 figures, accepted by RA