A note on some strong Whitney-reversible properties

All spaces considered in this paper are assumed to be metric. A continuum meas a compact connected space and a map means a continuous function. The letter X will always denote a continuum. Let c(X) denote the hyperspace ..

Beyond consistency test of gravity with redshift-space distortions at quasi-linear scales

Redshift-space distortions (RSD) offer an attractive method to measure the growth of cosmic structure on large scales, and combining with the measurement of the cosmic expansion history, it can be used as cosmological tests of gravity. With the advent of future galaxy redshift surveys aiming at precisely measuring the RSD, an accurate modeling of RSD going beyond linear theory is a critical issue in order to detect or disprove small deviations from general relativity (GR). While several improved models of RSD have been recently proposed based on the perturbation theory (PT), the framework of these models heavily relies on GR. Here, we put forward a new PT prescription for RSD in general modified gravity models. As a specific application, we present theoretical predictions of the redshift-space power spectra in f(R) gravity model, and compare them with N-body simulations. Using the PT template that takes into account the effects of both modifications of gravity and RSD properly, we successfully recover the fiducial model parameter in N-body simulations in an unbiased way. On the other hand, we found it difficult to detect the scale dependence of the growth rate in a model-independent way based on GR templates.Comment: 17 pages, 9 figures, version accepted for publication in PR

Asymptotic tails of massive scalar fields in Schwarzschild background

We investigate the asymptotic tail behavior of massive scalar fields in Schwarzschild background. It is shown that the oscillatory tail of the scalar field has the decay rate of $t^{-5/6}$ at asymptotically late times, and the oscillation with the period $2\pi/m$ for the field mass $m$ is modulated by the long-term phase shift. These behaviors are qualitatively similar to those found in nearly extreme Reissner-Nordstr\"{o}m background, which are discussed in terms of a resonant backscattering due to the space-time curvature.Comment: 21 pages, 2 figures, accepted for publication in Phys.Rev.

New route for synthesis of 3- and 5-caffeoylquinic acids via protected quinic acids

Caffeoylquinic acids (CQAs) are a group of the phenylpropanoids produced by certain plant species, which have various biological activities including antioxidant, antibacterial, anticancer, and others. Several synthetic routes have been developed using quinic acids (QAs) and caffeic acid derivatives as starting materials. In this study, alternative pathways of 3- and 5-CQAs preparation using protected quinic acids are described. Both CQAs were achieved by removal of the protecting groups of compound 9 and 18 with acid hydrolysis using dilute HCl solution. These compounds (9 and 18) are novel, resulted from esterification reaction of diacetyl caffeoyl chloride and protected quinic acids. The hydroxyl groups of quinic acid in this case were protected with 2,2-dimethoxy propane or tert-butyldimethylsilyl (TBS) chloride

Molecular Orientation in a Variable-Focus Liquid Crystal Lens Induced by Ultrasound Vibration

A method to estimate orientation direction of liquid crystal molecules three-dimensionally under ultrasound excitation was proposed and the relationship between the ultrasound vibration and the molecular orientation was discussed. Our group have reported a technique to control orientation direction of liquid crystal molecules using ultrasound vibration which could be applied to an optical variable-focus liquid crystal lens. The lens consisted of a liquid crystal layer sandwiched by two glass circular discs and a piezoelectric ring. Ultrasound vibration induces change in the refractive index of the lens, enabling the variable-focus function. The three-dimensional orientation direction of the liquid crystal molecules in the lens was predicted from the transmitted light distributions under the crossed Nicol conditions. The liquid crystal molecules were inclined from vertical alignment by the ultrasound vibration, and larger ultrasound vibration gave larger inclination of the molecules. There was a strong correlation between the distributions of ultrasound vibration and the liquid crystal molecular orientation; the molecular orientation was changed remarkably between the antinodal and nodal parts of the ultrasound flexural vibration on the glass plate and the molecules aligned towards the antinode