Caesium europium(III) polyphosphate, CsEu(PO3)4

Caesium europium polyphosphate, CsEu(PO3)4, was synthesized by a high-temperature solution reaction. Its structure is charaterized by a three-dimensional framework made up of double PO4 spiral chains and EuO8 and CsO11 polyhedra

Onset of chaotic gravitational lensing in non-Kerr rotating black holes with quadrupole mass moment

In the electromagnetic channel, chaotic gravitational lensing is a peculiar phenomenon in strong gravitational lensing. In this work, we analyze the properties and emergence of chaotic gravitational lensing in the Manko-Novikov black hole spacetime. Aiming to understand better the underlying physics, we elaborate on the boundaries of the accessible region in terms of the analyses of the contours of the effective potentials. The latter is associated with the two roots of a quadratic equation. In particular, we explore its interplay with ergoregion, which leads to specific features of the effective potentials, such as the emergence of cuspy edge and the formation of {\it pocket}, that serves as a static constraint on the geodesics. Besides, we investigate the properties of the radial and angular accelerations at the turning points in photons' trajectories. Moreover, the accelerations are analyzed, which is argued to provide a kinematic constraint on the geodesics. It is concluded that the onset of the chaotic lensing is crucially related to both constraints, and as a result, an arbitrarily slight deviation in the incident photon is significantly amplified during the course of evolution through an extensive period, demonstrating the complexity in the highly nonlinear deterministic gravitational system.Comment: 18 pages, 13 figure

The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects: Two assessment results

This research aimed to discuss the indigenous students’ learning effects of mathematics which was based on the self-designed localization and materialization of mathematics activities and had proceeded for one year. The quasi-experimental method was used in this research. There were 58 indigenous first grade students which were divided into three experimental groups (A, B, C) and one control group (D). Experimental instruments embodied written tests and manipulative tests which were designed by researchers according to the indicators proclaimed by Ministry of Education. The main findings were as followed: (1) The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects was limited. (2) According to the result of Paired T-test of the written and manipulative tests, most of scores of manipulative tests were higher written tests