Topological Structure of Fractal Squares

Given an integer $n\geq 2$ and a digit set ${\mathcal D}\subsetneq {0,1,...,n-1}^2$, there is a self-similar set $F \subset {\Bbb R}^2$ satisfying the set equation: $F=(F+{\mathcal D})/n$. We call such $F$ a fractal square. By studying a periodic extension $H= F+ {\mathbb Z}^2$, we classify $F$ into three types according to their topological properties. We also provide some simple criteria for such classification.Comment: 17 pages, 12 figure

Role of Hydrogen Bonding in Green Fluorescent Protein-like Chromophore Emission.

The fluorescence emission from green fluorescent protein (GFP) is known to be heavily influenced by hydrogen bonding between the core fluorophore and the surrounding side chains or water molecules. Yet how to utilize this feature for modulating the fluorescence of GFP chromophore or GFP-like fluorophore still remains elusive. Here we present theoretical calculations to predict how hydrogen bonding could influence the excited states of the GFP-like fluorophores. These studies provide both a new perspective for understanding the photophysical properties of GFP as well as a solid basis for the rational design of GFP-based fluorophores

Analytic study of superradiant stability of Kerr-Newman black holes under charged massive scalar perturbation

The superradiant stability of a Kerr-Newman black hole and charged massive scalar perturbation is investigated. We treat the black hole as a background geometry and study the equation of motion of the scalar perturbation. From the radial equation of motion, we derive the effective potential experienced by the scalar perturbation. By a careful analysis of this effective potential, it is found that when the inner and outer horizons of Kerr-Newman black hole satisfy $\frac{r_-}{r_+}\leqslant\frac{1}{3}$ and the charge-to-mass ratios of scalar perturbation and black hole satisfy $\frac{q}{\mu }\frac{Q}{ M}>1$, the Kerr-Newman black hole and scalar perturbation system is superradiantly stable.Comment: 7 pages, references adde

5-Fluoro-1H-indole-3-carb­oxy­lic acid

In the title compound, C9H6FNO2, the carboxyl group is twisted slightly away from the indole-ring plane [dihedral angle = 7.39 (10)°]. In the crystal, carboxyl inversion dimers linked by pairs of O—H⋯O hydrogen bonds generate R 2 2(8) loops and N—H⋯O hydrogen bonds connect the dimers into (10) sheets

A novel image encryption scheme based on Kepler’s third law and random Hadamard transform

In this paper, a novel image encryption scheme based on Kepler’s third law and random Hadamard transform is proposed to ensure the security of a digital image. First, a set of Kepler periodic sequences is generated to permutate image data, which is characteristic of the plain-image and the Kepler’s third law. Then, a random Hadamard matrix is constructed by combining the standard Hadamard matrix with the hyper-Chen chaotic system, which is used to further scramble the image coefficients when the image is transformed through random Hadamard transform. In the end, the permuted image presents interweaving diffusion based on two special matrices, which are constructed by Kepler periodic sequence and chaos system. The experimental results and performance analysis show that the proposed encrypted scheme is highly sensitive to the plain-image and external keys, and has a high security and speed, which are very suitable for secure real-time communication of image data