Geometrically distinct solutions for Klein–Gordon–Maxwell systems with super-linear nonlinearities

This paper is concerned with the following Klein–Gordon–Maxwell system $\left\{\begin{array}{c}-△u+V\left(x\right)u-(2\omega +\varphi )\varphi u=f(x,u),x\in {\mathbb{R}}^3,\hfill \\ △\varphi =(\omega +\varphi )u^2,x\in {\mathbb{R}}^3,\hfill \end{array}\right.$where $\omega >0$ is a constant, $V$ and $f$ are periodic with respect to $x$. By combining deformation type arguments, Lusternik–Schnirelmann theory and some new tricks, we prove that the above system admits infinitely many geometrically distinct solutions under weaker superlinear conditions instead of the common super-cubic conditions on $f$. Our result seems new and extends the previous results in the literature.     

“蓝瓶子”实验再探究*

利用SPSS 25.0统计软件对“蓝瓶子”实验进行正交实验设计,通过统计学分析得出最佳实验条件。利用氧化还原传感器(ORP)对“蓝瓶子”振荡体系的电极电势变化曲线进行分析,并针对蓝色的产生和消失过程设计3组对比实验深入探究,阐明其反应原理,意在引导学生深刻理解趣味实验现象背后的微观反应本质。     

Associating divisors with quadratic differentials on Klein surfaces

We extend the notion and basic properties of quadratic differential divisors to a Klein surface, using the corresponding form’s divisors from the double cover of the Klein surface.     

Ground state solutions for Klein–Gordon–Maxwell system with steep potential well

In this paper, we study the following Klein–Gordon–Maxwell system $\left\{\begin{array}{c}-\Delta u+(\lambda a\left(x\right)+1)u-(2\omega +\varphi )\varphi u=f(x,u),\mathrm{in}{\mathbb{R}}^3,\hfill \\ -\Delta \varphi =-(\omega +\varphi )u^2,\mathrm{in}{\mathbb{R}}^3.\hfill \end{array}\right.$Using variational methods, we obtain the existence of ground state solutions under some appropriate assumptions on $a$ and $f$.     

Simulating the Klein tunneling of pseudospin-one Maxwell particles with trapped ions

We propose an experimental scheme to simulate and observe the Klein tunneling of relativistic Maxwell particles with trapped ions. We explore the scattering dynamics of the pseudospin-one Maxwell particles and demonstrate that the scattered state should be a superposition of a reflection state, a localization state, and a transmission state. The probabilities of these states can be analytically obtained by the approach of Landau-Zener transition. We further show that the Maxwell Hamiltonian and the associated scattering dynamics can be mimicked with two trapped ions. The Maxwell spinors are encoded by three internal states of the first ion, the position and momentum are described by those of the motional modes, and the desired linear potential barrier is built by the second ion.     

气相色谱-质谱法测定聚对苯二甲酸乙二醇酯瓶装水中乙醛的迁移量

提出了测定聚对苯二甲酸乙二醇酯(PEGTP)瓶装纯水中乙醛迁移量的气相色谱质谱法。水样(100mL)中乙醛用2,4-二硝基苯肼在pH 3柠檬酸盐缓冲溶液10mL中,于40℃水浴上振荡1h加热使之衍生化。冷却后用二氯甲烷萃取3次,每次10mL。萃取液于40℃旋转蒸发至1.0mL,分取1分L进样分析。采用DB-5MS毛细管柱及在70℃～280℃范围内程序升温进行分离。线性范围在300μg·L~(-1)以内,检出限(3S/N)为1μg·L~(-1),加入50μg·L~(-1)及100μg·L~(-1)标准溶液做回收试验及精密度试验,测得平均回收率为88%,相对标准偏差(n=5)依次为5.4%及4.5%。     

Preparation and characterization of heat-resistant PET/bio-based polyester blends for hot-filled bottles

To improve the glass transition temperature (T_g) and heat resistance of polyethylene terephthalate (PET) bottle, poly (ethylene glycol 1,4-cyclohexane dimethylene isosorbide terephthalate) (PEICT) with a unique cyclic structure was introduced into PET. The miscibility of the PET/PEICT blends and their feasibility as a heat resistant bottle were investigated. The introduction of PEICT into PET increases the T_g and the PET/PEICT blends exhibit a single T_g, indicating good miscibility between PEICT and PET. Furthermore, the T_g and crystallinity of the PET/PEICT blends can be adjusted by controlling the amount of PEICT added. The PET/PEICT blends were transparent in the visible light range (no significant change in transparency) because the blends were truly miscible as confirmed by Fox equation. As expected, the introduction of PEICT into PET bottle allows for improved heat resistance and shape stability due to the rigid molecular structure and chirality of the two tetrahydrofuran rings in the isosorbide group of PEICT. Based on our results, the as-prepared PET/PEICT blends with controllable high heat resistance can be used as a cost-effective alternative material for various hot-filling conditions in the beverage industry by adjusting the optimal ratio of PEICT to PET for each product (e.g. fruit juice, tea).     

液体轴棱锥产生尺寸可调的单个局域空心光束

提出产生尺寸可调单个局域空心光束(bottle beam)的一种液体轴棱锥新模型.从几何光学角度分析了液体轴棱锥产生局域空心光束的原理,同时利用衍射理论加以模拟验证.得出:注入液体折射率大于轴棱锥材料折射率时可产生单个局域空心光束.通过光学设计软件TraeePro建立液体轴棱锥模型并模拟其光束传输变换特性.计算和模拟不...