Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

近紫外激发Gd2ZnTiO6∶Eu3+,Li+红色荧光粉的制备及荧光性能

采用溶胶-凝胶法成功制备出系列Eu³⁺掺杂和Li⁺、Eu³⁺共掺杂Gd₂ZnTiO₆红色荧光粉,并研究Li⁺、Eu³⁺掺杂对样品的晶体结构、微观形貌及发光性能的影响。结果显示,所制备的Gd₂ZnTiO₆∶Eu³⁺,Li⁺(GZT∶Eu³⁺,Li⁺) 荧光粉为双钙钛矿结构,属于单斜晶系(空间群:P2₁/n),大小为10 μm的无规则形状的颗粒。在395 nm近紫外光的激发下,GZT∶Eu³⁺的发射光谱展示出典型的Eu³⁺线状特征光谱,发射峰中心位于615 nm处,归属于Eu³⁺的⁵D₀→⁷F₂跃迁。Eu³⁺的最佳掺杂浓度为0.07(摩尔分数),样品显示明显的浓度猝灭效应,其机制为电偶极子-电偶极子(d-d)相互作用。此外,研究还发现,Li⁺掺杂对样品的晶体结构、微观形貌没有影响,但是一定量的Li⁺掺杂可以显著增强样品的荧光强度。当Li⁺浓度为0.05时,荧光粉发射主峰强度增强程度最大,提高至原来的4.3倍,说明通过Li⁺、Eu³⁺共掺杂可以获得高亮度的GZT红色荧光粉。GZT∶0.14Eu³⁺,0.05Li⁺荧光粉的CIE色坐标为(0.631 1,0.375 3)与标准红光色坐标(0.670,0.330)较为接近,是一种潜在的LED用红色荧光粉。     

A Normal Criterion Concerning Omitted Holomorphic Function

In this paper, we continue to discuss the normality concerning omitted holomorphic function and get the following result. Let F be a family of meromorphic functions on a domain D, k ≥ 4 be a positive integer, and let a(z) and b(z) be two holomorphic functions on D, where a(z) 0 and f(z) ≠ ∞ whenever a(z)=0. If for any f ∈ F, f'(z) -a(z)f^k(z) ≠ b(z), then F is normal on D.     

Addition-elimination of nitroalkanes to 3-phenacylideneoxindoles—direct method for the synthesis of 3-alkenylphenacylidene-oxindoles

The first addition-elimination of nitroalkanes to 3-phenacylideneoxindoles was developed, affording the corresponding 3-alkenylphenacylidene-oxindoles with high yields.The addition-elimination mechanism of 3-phenacylideneoxindoles with nitroalkanes and removable NO₂ group in concert guarantees the high regioselectivity.     

Mono-components from Blaschke products as solutions of a wave equation

In this note, we prove that the uni-modular mono-components from Blaschke products in the unit disc are eigenvectors of the Sturm-Liouville operators and investigate a kind of wave equations with some initial conditions, which give rise to mono-components.     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

Recent progress in advanced core-shell metal-based catalysts for electrochemical carbon dioxide reduction

Electrochemical carbon dioxide reduction（CO₂RR） plays an important role in solving the problem of high concentration of CO₂in the atmosphere and realizing carbon cycle. Core-shell structure has many unique features including tandem catalysis, lattice strain effect, defect engineering, which exhibit great potential in electrocatalysis. In this review, we focus on the advanced core-shell metal-based catalysts（CMCs） for electrochemical CO₂RR. The recent progress of ...     

Selective oxidation of benzylic,allylic and propargylic alcohols using dirhodium(II) tetraamidinate as catalyst and aqueous tert‐butyl hydroperoxide as oxidant

We show that the dirhodium(II) tetraamidinate complex Rh₂(Msip)₄ efficiently catalyzes the oxidation of activated secondary alcohols at only 0.1 mol% loading. In this approach, we oxidized various benzylic, allylic and propargylic alcohols to the corresponding carbonyl compounds under mild aqueous conditions using the inexpensive oxidant T‐HYDRO® (70 wt% aqueous tert‐butyl hydroperoxide). Copyright © 2015 John Wiley & Sons, Ltd.