Reheating after f(R) inflation

The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.Comment: 16 pages, 11 figure

A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 page

Digital microscopy: A useful technique for measuring root elongation in solution

Decreased root elongation and rupture of outer cells, major effects of soluble aluminum (Al), may be studied using digital microscopy with little interference by the experimental technique. Single roots of 3-d-old mungbean (Vigna radiata L.) or soybean (Glycine max (L.) Merr.) seedlings were marked with activated charcoal particles and grown for ca. 2 h in 500 mL 1 mM CaCl solution at pH 6, followed by the imposition of an Al treatment. A digital image at 25-time magnification was recorded every 5 min for up to 7 h. Examination of the digital images showed that Al exerted its rhizotoxic effects rapidly (ca. 20-50 min) by reducing cell expansion in the elongation zone. Rupture of epidermal and outer cortical cells occurred later (after≥4 h) and closer to the root tip. Digital microscopy has a number of inherent benefits and problems, but is overall a valuable technique that may find wide use in studies on root growth

A manifesto for researching entrepreneurial ecosystems

Entrepreneurial ecosystems are the focus of government economic policies around the world for their potential to generate entrepreneur-led economic development. The paper identifies key research questions and challenges to building effective public policy: (i) the limitations of existing data sources, (ii) the need to balance findings from quantitative and qualitative studies, (iii) the danger that entrepreneurial ecosystems will be just a policy fad, (iv) the narrow focus of policy and research on high tech firms and scale-ups, and (v) the need to balance research approaches between simplified models and a complex systems approach. There is a need for a better understanding of the diversity of policy contexts (level of government, country context) and model of ecosystem governance. A more granulated understanding of ecosystem thinking is required, with greater consideration of the diversity of actors and the institutional context, with more attention given to the heterogeneous nature of places and complex interactions between actors and networks. Looking to the future, the potential of new data sources and methodologies is identified. Future research should give greater consideration to the institutional context to understand how policy can better support entrepreneurial activity and the extent to which specific policies can be replicated elsewhere

Testing metric-affine f(R)-gravity by relic scalar gravitational waves

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against sensitivities of VIRGO, LIGO and LISA interferometers.Comment: 12 pages, 4 figure

Optimal Location of Two Laser-interferometric Detectors for Gravitational Wave Backgrounds at 100 MHz

Recently, observational searches for gravitational wave background (GWB) have been developed and given constraints on the energy density of GWB in a broad range of frequencies. These constraints have already resulted in the rejection of some theoretical models of relatively large GWB spectra. However, at 100 MHz, there is no strict upper limit from direct observation, though an indirect limit exists due to He4 abundance due to big-bang nucleosynthesis. In our previous paper, we investigated the detector designs that can effectively respond to GW at high frequencies, where the wavelength of GW is comparable to the size of a detector, and found that the configuration, a so-called synchronous-recycling interferometer is best at these sensitivity. In this paper, we investigated the optimal location of two synchronous-recycling interferometers and derived their cross-correlation sensitivity to GWB. We found that the sensitivity is nearly optimized and hardly changed if two coaligned detectors are located within a range 0.2 m, and that the sensitivity achievable in an experiment is far below compared with the constraint previously obtained in experiments.Comment: 17 pages, 6 figure

Alternating-Spin Ladders in a Magnetic Field: New Magnetization Plateaux

We study numerically the formation of magnetization plateaux with the Lanczos method in 2-leg ladders with mixed spins of magnitudes $(S_1,S_2)=(1,1/2)$ located at alternating positions along the ladder and with dimerization $\gamma$. For interchain coupling $J'>0$ and $\gamma=0$, we find normalized plateaux at $m=1/3$ starting at zero field and $m=1$ (saturation), while when $\gamma \ne 0$ is columnar, another extra plateau at $m=2/3$ shows up. For $J'<0$, when $\gamma<\gamma_c(J')$ we find no plateau while for $\gamma>\gamma_c(J')$ we find four plateaux at $m=0,1/3,2/3,1$. We also apply several approximate analytical methods (Spin Wave Theory, Low-Energy Effective Hamiltonians and Bosonization) to understand these findings and to conjeture the behaviour of ferrimagnetic ladders with a bigger number of legs.Comment: REVTEX file, 7 pages, 6 eps Figure

Optical properties of substituted phthalocyanine rare-earth metal complexes

Comparative study of optical properties of alkylthio-group-substituted phthalocyanine rare-earth metal sandwich complexes ([(CnS)8Pc]2M,M=Eu,Lu,Tb) is presented. Photoluminescence and photoconductivity of [(CnS)8Pc]2M complex is very weak. Two photoluminescence bands were observed at around 400–650 and 720–800 nm in chloroform solution corresponding to the Soret and Q bands in the absorption spectra, respectively. However, the emission from Eu3+ ion (as well as Tb3+) was not found compared with other Eu complexes because the 5d levels of the Eu3+ ion lie higher than the triplet level of the ligand. The significant enhancement of the photoconductivity of [(C16S)8Pc]2M after C60 doping is reported. The photoconductivity is positive at the low electric field in the ohmic regime while it becomes negative at the high electric field upon photoexcitation with strongly absorbed light. The negative photoconductivity is attributed to space-charge effects. The mechanism of photoluminescence and photoconductivity are discussed by taking the electronic energy schemes of phthalocyanine ligands and lanthanide ion and C60 into consideration.This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in K. Yoshino, S. B. Lee, T. Sonoda, H. Kawagishi, R. Hidayat, K. Nakayama, M. Ozaki, K. Ban, K. Nishizawa, K. Ohta, and H. Shirai, Journal of Applied Physics 88, 7137 (2000) and may be found at https://doi.org/10.1063/1.1316050