Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

离子液体在大气压等离子体中稳定性研究

采用发射光谱、紫外可见吸收光谱、红外吸收光谱和核磁共振技术分析1-丁基-3-甲基咪唑硫酸氢盐（[Bmim]HSO₄）, 1-丁基吡啶硫酸氢盐（HSO₄）和1-丁基-3-甲基咪唑四氟化硼（[Bmim]BF₄）三种离子液体在大气压介质阻挡放电氩等离子体体系中的稳定性，并分别以上述三种离子液体为辅助液采用大气压介质阻挡放电等离子体技术制备TiO₂，进一步研究三种离子液体在等离子体中的稳定性对所制备的TiO₂晶相结构的影响。结果表明：向大气压介质阻挡放电氩等离子体中分别引入[Bmim]HSO₄，HSO₄和[Bmim]BF₄离子液体后并未改变氩等离子体放电光谱谱峰的位置和数量且没有新的谱峰生成，但谱峰强度都明显降低，说明上述三种离子液体没有在等离子体区蒸发形成激发态物种；[Bmim]HSO₄和HSO₄放电前后的红外吸收光谱基本一致，表明离子液体在放电后的化学键未发生改变；[Bmim]HSO₄和HSO₄的紫外可见吸收光谱显示其吸收峰的位置和强度未发生改变，说明两种离子液体在等离子体作用后的结构是稳定的；[Bmim]BF₄放电前后的红外吸收光谱各个特征峰并无明显差异，但其紫外可见吸收光谱图谱吸收峰的位置却发生较大的偏移，进一步对放电前后的[Bmim]BF₄离子液体进行核磁共振分析，两者的1H NMR峰数相同，但放电后的离子液体化学位移向高位偏移大约0.2单位，说明其化学环境发生了变化，表明有部分[Bmim]BF₄结构发生改变。光谱和核磁共振技术分析表明离子液体[Bmim]BF₄在等离子体作用后结构发生了改变。采用三种离子液体辅助大气压介质阻挡放电等离子体技术制备TiO₂样品的X-射线衍射分析结果表明 [Bmim]HSO₄和HSO₄辅助制备的HSO₄-TiO₂和[Bmim]HSO₄-TiO₂，谱图与锐钛矿相TiO₂标准谱图基本一致，表明所制备的TiO₂为纯锐钛矿型。而[Bmim]BF₄辅助制备的[Bmim]BF₄-TiO₂在2θ=24.1°处的衍射峰向小角度偏移，2θ=48°处的衍射峰向大角度偏移，说明[Bmim]BF₄在辅助制备TiO₂过程中，F进入TiO₂的晶格，破坏了TiO₂原子间的平衡状态，生成了F掺杂TiO₂光催化材料。F掺杂TiO₂光催化材料的形成也间接证明了离子液体[Bmim]BF₄在大气压等离子体中的不稳定性，此结果与核磁共振及紫外可见光的检测结果相一致。同时说明离子液体在等离子体的作用下对于纯锐钛矿晶格的形成和促进高活性掺杂型的光催化材料具有重要作用。为等离子体辅助离子液体制备高性能纳米材料提供重要的实验和理论依据。     

A New Planar Hexanuclear Dysprosium Cluster Exhibiting Slow Magnetic Relaxation Features

Reaction of the Schiff base ligand H₂L and dysprosium acetate result in a new planar Dy₆ cluster [Dy₆(μ₃‐OH)L₆(Ac)₆] · MeOH ( 1 ) [H₂L = N'‐(2‐hydroxybenzylidene)‐2‐(hydroxyimino)propanohydrazide, HAc = acetic acid], which was successfully structurally and magnetically characterized. Single‐crystal X‐ray diffraction analysis revealed that 1 contained a hexanuclear dysprosium cluster [Dy₆], which is composed of four Dy₃ triangular units. Magnetic measurements suggest that 1 displays single‐molecule magnet (SMM) behavior which is enhanced by applying a 4000 Oe direct‐current field. The effective anisotropic barrier U_eff/k_B = 14.9 K and the pre‐exponential factor τ₀ = 1.31 × 10^–6 s are also obtained. This work may provide more insights for the design and investigation of lanthanide‐based SMMs.     

Dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate liquid crystal

The dielectric and elastic properties of liquid crystals (LCs) generally depend on the molecule structure, such as polar group and carbon chain length. For further investigation of the influence of molecular structure on the dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate LC, the experimental temperature was controlled at 25°C by precision hot stage, and a precision LCR meter was used to measure the capacitance of six LC cells under the voltage from 0.1 to 20 V at 1 kHz. An LC cell capacitance model and a dual-cell model were adopted to obtain the dielectric anisotropy, and the capacitance–voltage curves of six LC materials were plotted. The threshold voltage of Fréedericksz transition was analysed, and a finite difference iterative method was used to attain specific values of three elastic constants. The influence of molecular structure on the dielectric and elastic constants was finally analysed. Experimental results showed that the introduction of meta-difluoro group would increase the dielectric anisotropy and reduce the threshold voltage of LC. As the length of the alkyl carbon chain increased, the dielectric anisotropy would have an odd–even alternation effect, which would lead to changes in the elastic constants of LC.     

Novel low-dielectric constant and soluble polyimides from diamines containing fluorene and pyridine unit

Polyimides (PI's) with low-dielectric constant and excellent organic solubility have broad application prospects in the electronic field. Herein, this study designed a series of novel, low dielectric, organic soluble PI films by creatively introducing fluorene and pyridine ring into diamine monomers. Because of the noncoplanar structure of fluorenyl and the polarization of pyridine ring, PI films achieved a low-dielectric constant (2.22–3.09 at 10 MHz) and excellent organic solubility. Even in some organic solvents with low-boiling points, these PI films still exhibited outstanding solubility. In addition, all the films possessed high-tensile strength (≈120 MPa) and excellent optical transparency (>70%, 450 nm). It was worth noting that the glass transition temperature of films was all above 280°C and 5% weight loss temperature (T_5%) was at 486–553°C. In general, the novel high-performance low-dielectric PI films are expected to be used in the field of microelectronics.     

光栅衍射实验中测量光栅常数的两种辅助方法

衍射光栅可以将不同波长的光在空间上分离开,在光谱分析领域中有广泛应用.利用光栅的衍射来测量光栅常数是大学物理实验中的一个典型实验,而本文介绍的正是光栅衍射实验中的两个有趣现象:一是旋转光栅时,谱线的偏转角存在一个最小值;二是光栅旋转到一定角度时,衍射光斑会逐渐消失在视野中.论文从理论上分析解释这两种现象,并设计出两种测量光栅常数的方法,在实验上进行验证.与传统的用最小偏转角测光栅常数的方法相比,本文重点分析了由判定最小偏转角位置偏差所带来的影响,并提出了对称旋转测量的方法来进一步减小误差.     

Fast Cysteine Bioconjugation Chemistry

Cysteine bioconjugation serves as a powerful tool in biological research and has been widely used for chemical modification of proteins, constructing antibody-drug conjugates, and enabling cell imaging studies. Cysteine conjugation reactions with fast kinetics and exquisite selectivity have been under heavy pursuit as they would allow clean protein modification with just stoichiometric amounts of reagents, which minimizes side reactions, simplifies purification and broadens functional group tolerance. In this concept, we summarize the recent advances in fast cysteine bioconjugation, and discuss the mechanism and chemical principles that underlie the high efficiencies of the newly developed cysteine reactive reagents.     

量子垒生长速率对InGaN基绿光LED性能的影响

利用MOCVD技术在图形化Si(111)衬底上生长了InGaN/GaN绿光LED外延材料。在GaN量子垒的生长过程中,保持NH3流量不变,通过调节三乙基镓(TEGa)源的流量来改变垒生长速率,研究了量子垒生长速率对LED性能的影响。使用二次离子质谱仪(SIMS)和荧光显微镜(FLM)分别对量子阱的阱垒界面及晶体质量进行了表征,使用电致发光测试系统对LED光电性能进行了表征。实验结果表明,垒慢速生长,在整个测试电流密度范围内,外量子效率(EQE)明显提升。我们认为,小电流密度下,EQE的提升归结为量子阱晶体质量的改善;而大电流密度下,EQE的提升则归结为阱垒界面陡峭程度的提升。     

Emergence of a non-Fowler-Nordheim-type behavior for a general planar tunneling barrier

In this work we investigate a generalized tunneling barrier for planar emitters at zero-temperature. We present the evidence of the emergence of a non-Fowler-Nordheim-type general behavior for the field emission current density in the case that the Fermi energy (μ) is comparable with or smaller that the decay width ($d_F$). Therefore, for some non-metals or materials that have very small Fermi energy the standard Fowler-Nordheim-type theory may require a correction. In the opposite regime, i.e., for μ much larger that $d_F$, we confirm that the conventional theory is suitable for metals.     

Properties of RhP predicted by first-principles

Using density functional theory combined with a global crystal structure search with the particle swarm optimization method, we propose three stable three-dimensional (3D) metallic RhP structures, namely, the Cmcm (RhP-I), P6/mmm (RhP-II), and P6₃mc (RhP-III) phases. All these structures are found to be dynamically stable through vibrational normal mode calculations, indicating that they could be successfully synthesized in experiments. We show that the RhP-I phase has a relatively high thermodynamic stability and high mechanical strength in comparison with the others. The RhP-II and RhP-III phases have porous structures which could accommodate small atoms or molecules. However their thermodynamics are poor, especially the RhP-III phase. The RhP-II structure is stable at 500 K, but the RhP-III fails to survive even at the freezing point of water. Importantly, all these materials have one dimensional conducting channels corresponding to ultrahigh Fermi velocities. Moreover, the porous hexagonal RhP-II and III structures exhibit excellent ability to trap lithium, hydrogen, oxygen, and boron atoms. The RhP-II structure could be especially useful for directly dissociating the hydrogen molecule into two atoms without an energy barrier. In the present study, we identify three new metallic structures to the family of RhP structures, and anticipate their potential for technological applications.