On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups

Let G be a finite group and (G) the set of the numbers of conjugates of noncyclic proper subgroups of G. We prove that (1) if |(G)|≤2, then G is solvable, and (2) G is a nonsolvable group with |(G)|=3 if and only if G≅PSL(2,5) or PSL(2,13) or SL(2,5) or SL(2,13)

Possible discovery of the r-process characteristics in the abundances of metal-rich barium stars

We study the abundance distributions of a sample of metal-rich barium stars provided by Pereira et al. (2011) to investigate the s- and r-process nucleosynthesis in the metal-rich environment. We compared the theoretical results predicted by a parametric model with the observed abundances of the metal-rich barium stars. We found that six barium stars have a significant r-process characteristic, and we divided the barium stars into two groups: the r-rich barium stars ($C_r>5.0$, [La/Nd]\,$<0$) and normal barium stars. The behavior of the r-rich barium stars seems more like that of the metal-poor r-rich and CEMP-r/s stars. We suggest that the most possible formation mechanism for these stars is the s-process pollution, although their abundance patterns can be fitted very well when the pre-enrichment hypothesis is included. The fact that we can not explain them well using the s-process nucleosynthesis alone may be due to our incomplete knowledge on the production of Nd, Eu, and other relevant elements by the s-process in metal-rich and super metal-rich environments (see details in Pereira et al. 2011).Comment: 5 pages, 5 figures, accepted for publication in A&

Uniaxial and Mixed Orientations of Poly(ethylene oxide) in Nanoporous Alumina Studied by X-ray Pole Figure Analysis

The orientation of polymers under confinement is a basic, yet not fully understood phenomenon. In this work, the texture of poly(ethylene oxide) (PEO) infiltrated in nanoporous anodic alumina oxide (AAO) templates was investigated by X-ray pole figures. The influence of geometry and crystallization conditions, such as pore diameter, aspect ratio, and cooling rates, was systematically examined. All the samples exhibited a single, volume-dependent crystallization temperature (Tc) at temperatures much lower than that exhibited by bulk PEO, indicating “clean” microdomains without detectable heterogeneous nucleation. An “orientation diagram” was established to account for the experimental observations. Under very high cooling rates (quenching), crystallization of PEO within AAO was nucleation-controlled, adopting a random distribution of crystallites. Under low cooling rates, growth kinetics played a decisive role on the crystal orientation. A relatively faster cooling rate (10 °C/min) and/or smaller pores lead to the * ║ pore axis (n⃗) mode (uniaxial orientation). When the cooling rate was lower (1 °C/min), and/or the pores were larger, a mixed orientation, with a coexistence of * ║ n⃗ and * ║ n⃗ , was observed. The results favor the kinetic model where the fastest growth direction tends to align parallel to the pore axis.This work is supported by the National Natural Science Foundation of China (NSFC, 21873109, 51820105005, 21274156). G. L. is grateful to the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2015026). G. L., D. W., and A. J. M. also acknowledge European funding by the RISE BIODEST project (H2020-MSCA-RISE-2017-778092). The authors thank Dr. Zhongkai Yang for assistance with pole figure measurement

Static and dynamic material properties of CFRP/epoxy laminates

Carbon fiber reinforced polymer (CFRP) has been extensively used to strengthen structures owing to its outstanding mechanical properties. With an increasing threat from terrorist bombing attacks and accidental explosions, the application of CFRP has been extended to mitigate the effect of blast loading on structures. A better understanding of the dynamic material properties of CFRP/epoxy laminates at high strain rates is therefore needed for more reliable analysis and design of CFRP strengthened structures under dynamic loadings. In this study, the unidirectional tensile properties of CFRP (SikaWrap®-230C) and epoxy resin (Sikadur®-330) laminates is investigated experimentally over a wide range of strain rates. Quasi-static and low-speed tensile tests are conducted at strain rates varying from 7 × 10−5 s−1 to 0.07 s−1. Then, high-speed tensile tests are performed using a high-speed servo-hydraulic testing machine at strain rate from about 10 s−1 to 240 s−1. The testing results show that both the tensile strength and the stiffness of the CFRP/epoxy laminates are insensitive to loading speed when the strain rate is less than 50 s−1. However, when strain rate is over 50 s−1, both the tensile strength and the coupon stiffness increase with the increase of strain rate. High-speed camera images are used to assist inspecting the failure modes of CFRP/epoxy laminates. It is found that under high-strain rate tension CFRP/epoxy laminates fail differently from that at low-strain rate. The different failure mode is believed to contribute to the increment of laminate strength. The testing data are analyzed together with available testing results on CFRP/epoxy laminates at various strain rates. Empirical formulas of dynamic increase factor for CFRP material are derived for better prediction of material strength at various strain rates