Codimension two bifurcation of a vibro-bounce system

A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.The project supported by the National Natural Science Foundation of China (10172042, 50475109) and the Natural Science Foundation of Gansu Province Government of China (ZS-031-A25-007-Z (key item))     

Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

The Ramanujan Journal - In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of...     

Strong Pauli paramagnetic effect in the upper critical field of KCa2Fe4As4F2

Recently, 12442 system of Fe-based superconductors has attracted considerable attention owing to its unique double-Fe As-layer structure. A steep increase in the in-plane upper critical field with cooling has been observed near the superconducting transition temperature, Tc, in KCa2Fe4As4F2 single crystals. Herein, we report a high-field investigation on upper critical field of this material over a wide temperature range, and both out-of-plane(H∥c, Hc2c) and in-plane(H∥ab, Hc2ab ) directions have been measured.A sublinear temperature-dependent behavior is observed for the out-of-plane Hc2c , whereas strong convex curvature with cooling is observed for the in-plane Hc2ab . Such behaviors could not be described by the conventional Werthamer-Helfand-Hohenberg(WHH) model. The data analysis based on the WHH model by considering the spin aspects reveals a large Maki parameter α=9,indicating that the in-plane upper critical field is affected by a very strong Pauli paramagnetic effect.     

窄线宽光纤激光器在1030 nm波段实现3 kW近衍射极限输出

基于大模场面积掺镱光纤搭建了全光纤1030 nm高功率窄线宽光纤激光主振荡功率放大系统,实现了3004 W的最高功率输出,斜率效率69.27%,是目前报道的输出功率最高的1030 nm波段近衍射极限光纤激光器。最高输出功率时,x,y方向的光束质量因子分别为1.169,1.174,3 dB光谱宽度为0.18 nm,放大自发辐射抑制比达到37 dB。     

M2B7-(M=Mg,Zn)团簇的双重芳香性促进Mg-Mg和Zn-Zn单键的形成

本文使用密度泛函理论设计了两个无需配体的具有Mg-Mg和Zn-Zn单键的团簇Mg₂B₇^-和Zn₂B₇^-. 这两种团簇的全局能量最低构型均以M₂²⁺(B₇^3-)的形式存在，其中M-M单键处于准平面六边形形状的B₇部分的上方. 化学键分析证实了这些团簇中Mg-Mg和Zn-Zn单键的存在，这些单键是在异常稳定的B₇^3-的驱动下生成的. 该B₇^3-部分同时具有σ和π双重芳香性. 计算得到Mg₂B₇^-和Zn₂B₇^-的垂直跃迁能分别为2.79 eV和2.94 eV.     

Facile synthesis of thermosensitive functional polyaspartamide derivatives by click chemistry

Biodegradable and thermosensitive polyaspartamide derivatives containing pendant azide groups P(Asp‐Az)_X‐HPAs were synthesized from poly(l ‐succinimide) via the ring‐opening reaction with 2‐azidoethylamine (Az) and 5‐hydroxypentylamine (HPA). Then hydrophobic phenethyl (PEA) and imidazole (IMZ) moieties were introduced successfully with very high reaction efficiency above 90% to the side chains of P(Asp‐Az)_X‐HPA by click reaction to obtain thermoresponsive polyaspartamide derivatives containing pendant aromatic rings P(Asp‐Az)_X‐HPA‐PEAs and the thermo/pH‐responsive polyaspartamide derivatives containing pendant imidazole rings P(Asp‐Az)_X‐HPA‐IMZs, respectively. The thermoresponsive behaviors of P(Asp‐Az)_X‐HPA‐PEAs and P(Asp‐Az)_X‐HPA‐IMZs were confirmed by dynamic light scattering (DLS) and transmittance measurements, and the cloud point can be tuned by designed amounts of azide groups and can be further adjusted by the grafting molar percentage of hydrophobic phenethyl or imidazole moieties to the side chains of P(Asp‐Az)_X‐HPA via click chemistry. The pH‐responsive behavior of P(Asp‐Az)_X‐HPA‐IMZs can also be tuned. These results indicate that the obtained polyaspartamide‐based functional polymers can be further functionalized with hydrophilic long PEG chain and/or targeted moieties via click chemistry for drug delivery. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1296–1303     

Negative slope of resistivity–temperature curve and positive magnetoresistance in antiperovskite ZnCNi3−x Mn x (1.15≤x≤1.5)

In antiperovskite intermetallics ZnCNi_3?x Mn _x , the negative slope coefficient (NSC) dρ/dT of resistivity–temperature curves is observed when x=1.15,1.25,1.4,1.5. The sample with x=1.25 shows a semiconductor-like behavior in the whole temperature range of 15–290 K. By study of the magnetization, magnetoresistance, and low-temperature X-ray diffraction, it is found that Mn dopant significantly affects the physical properties of ZnCNi_3?x Mn _x by changing both the carrier density and the magnetism. The origin of the NSC dρ/dT can be ascribed to the change of hole-like carrier density, which is adjusted by Mn content. The existence of hole-like carriers can be understood rationally by the two-band model. The change of sign of magnetoresistance from positive to negative has been observed in ZnCNi_3?x Mn _x with the change of Mn content, which could be ascribed to the competition between the contribution from field-induced suppression of the thermally excited ferromagnetic spin fluctuations and the Lorentz contribution. When Mn content is low, the Lorentz contribution dominates the sign of magnetoresistance. On the other hand, when Mn content is high, the contribution from field-induced suppression of the thermally excited ferromagnetic spin fluctuations dominates the sign of magnetoresistance.