Existence and uniqueness of nontrivial solutions for eigenvalue boundary value problem of nonlinear fractional differential equation

In this paper, we study the existence and uniqueness of a nontrivial solution to eigenvalue problems for the following nonlinear fractional differential equation of the form $$\begin{aligned} \left\{ \begin{array}{l} -D^{\alpha }_{0^{+}}u(t)=\lambda [f(t, u(t), D^{\beta }_{0^{+}}u(t))+g(t)],~~ 0 where \(\lambda \) is a parameter, \(D^{\alpha }_{0^{+}},D^{\beta }_{0^{+}}\) are two standard Riemann–Liouville fractional derivatives, \(0<\beta <1<\alpha \le 2,\alpha -\beta >1,f: [0,1]\times {\mathbb{R }}\times {\mathbb{R }}\rightarrow {\mathbb{R }}\) is continuous, and \(g(t): (0, 1)\rightarrow [0, +\infty )\) is Lebesgue integrable. We obtain several sufficient conditions of the existence and uniqueness of nontrivial solution of the above eigenvalue problems when \(\lambda \) is in some interval. Our approach is based on the Leray–Schauder nonlinear alternative. In addition, some examples are included to demonstrate the main result.     

Single-mode low-loss optical fibers for long-wave infrared transmission

In this Letter, we report single-mode fibers made of chalcogenide glasses with low loss in the 5-12μm range. Glasses from the Ge-As-Te-Se system were optimized to prevent nucleation and to exhibit low density of charge carriers. Single-mode fibers were obtained through the rod-in-tube method by substituting 2% Te/Se between the core and cladding glasses. The resulting single-mode fibers had a core diameter of 30μm and exhibited losses of ~6 dB/m at 10.6μm, and as low as 3-4dB/m in the 6-10μm range.     

A diffractive study of optical parametric interactions in nonlinear photonic crystals

With the nonlinear diffraction concept, we present a diffractive study of optical parametric interactions in nonlinear photonic crystals. The nonlinear diffraction concept enables the design of complicated nonlinear photonic crystal structures in an intuitive way. We show that there are two basic linear sequences, the anti-stacking and the para-stacking sequences, existing in a one-dimensional structure; and we present the realization of multiple phase-matching resonances in the combination of the two basic sequences. The parameters affecting the structure factor of a two-dimensional nonlinear photonic crystal are investigated, which indicate that not only the Ewald construction but also the relative domain size determines two-dimensional nonlinear diffractions.     

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics简

In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.     

不同磁路电子回旋共振离子源引出实验

空间推进所用的电子回旋共振离子源(ECRIS)应具有体积小、效率高的特点. 本文研究的ECRIS使用永磁体环产生磁场, 有效减小了体积, 该离子源利用微波在磁场中加热电子, 电子与中性气体发生电离碰撞产生等离子体. 磁场在微波加热电子的过程中起关键作用, 同时影响离子源内等离子体的约束和输运. 通过比较四种磁路结构离子源的离子电流引出特性来研究磁场对10 cm ECRIS性能的影响. 实验发现: 在使用氩气的条件下, 特定结构的离子源可引出160 mA的离子电流, 最高推进剂利用率达60%, 最小放电损耗为120 W·A^-1; 所有离子源均存在多个工作状态, 工作状态在微波功率、气体流量、引出电压变化时会发生突变. 离子源发生状态突变时的微波功率、气体流量的大小与离子源内磁体的位置有关. 通过比较不同离子源的引出离子束流、放电损耗、气体利用率、工作稳定性的差异, 归纳了磁场结构对此种ECRIS引出特性的影响规律, 分析了其中的机理. 实验结果表明: 保持输入微波功率、气体流量、引出电压不变时, 增大共振区的范围、减小共振区到栅极的距离, 离子源能引出更大的离子电流; 减小共振区到微波功率入口、气体入口的距离能降低维持离子源高状态所需的最小微波功率和最小气体流量, 提高气体利用率, 但会导致放电损耗增大. 研究结果有助于深化对此类离子源工作过程的认识, 为其设计和性能优化提供参考.     

Influence of assortativity and degree-preserving rewiring on the spectra of networks

Newman’s measure for (dis)assortativity, the linear degree correlation coefficient $\rho _{D}$ , is reformulated in terms of the total number N _k of walks in the graph with k hops. This reformulation allows us to derive a new formula from which a degree-preserving rewiring algorithm is deduced, that, in each rewiring step, either increases or decreases $\rho _{D}$ conform our desired objective. Spectral metrics (eigenvalues of graph-related matrices), especially, the largest eigenvalue $\lambda _{1}$ of the adjacency matrix and the algebraic connectivity $\mu _{N-1}$ (second-smallest eigenvalue of the Laplacian) are powerful characterizers of dynamic processes on networks such as virus spreading and synchronization processes. We present various lower bounds for the largest eigenvalue $\lambda _{1}$ of the adjacency matrix and we show, apart from some classes of graphs such as regular graphs or bipartite graphs, that the lower bounds for $\lambda _{1}$ increase with $\rho _{D}$ . A new upper bound for the algebraic connectivity $\mu _{N-1}$ decreases with $\rho _{D}$ . Applying the degree-preserving rewiring algorithm to various real-world networks illustrates that (a) assortative degree-preserving rewiring increases $\lambda _{1}$ , but decreases $\mu _{N-1}$ , even leading to disconnectivity of the networks in many disjoint clusters and that (b) disassortative degree-preserving rewiring decreases $\lambda _{1}$ , but increases the algebraic connectivity, at least in the initial rewirings.     

Structural and superconductivity study on α-FeSex

We have successfully synthesized the α-FeSe_x binary tetragonal superconductors with nominal composition of FeSe_x (x=0.6-1.0) via conventional solid state reactions between Fe and Se sealed in quartz tubes. Fe and β-FeSe are the most commonly seen impurities in this binary system. A low-temperature annealing at 400 °C is found to be crucial to remove β-FeSe, which is the thermodynamic stable phase with hexagonal symmetry. For all the samples of FeSe_x, superconductivity is confirmed by magnetic measurements as well as resistivity measurements with their T_c at around 8 K. We noticed that their T_c does not vary with the different nominal Se amount. High-resolution synchrotron X-ray diffraction analysis revealed that the unit cell parameters of all these samples do not change within the error range, and their structure only tolerate the same very small amount of Se deficiency. Based on this study, we concluded that the α-FeSe_x superconductor only exist in a very narrow deficiency range.     

O-vacancy and surface on CeO2: A first-principles study

Atomic and electronic structures of CeO₂ (1 1 1), (1 1 0) and (1 0 0) surfaces are investigated using the first-principles density functional theory taking into account the on-site Coulomb interaction. Both the stoichiometric and O-deficient surfaces are examined in order to clarify the overall features. The CeO₂ (1 1 1) is found to be the most stable surface, followed by the (1 1 0) and (1 0 0) surfaces, consistent with experimental observations. Three surfaces exhibit different features of relaxation. Large relaxations are found at the (1 1 0) and (1 0 0) surfaces, while very small changes are observed at the (1 1 1) surface. It is found that the O-vacancy occurs more readily at the (1 1 0) surface as compared with the (1 1 1) surface. Furthermore, the formation energies of the O-vacancy in the surfaces are lower than that in the bulk. The energetically favorable O-vacancy locates in the second O-atomic layer for the (1 1 1) while at the surface layer for the (1 1 0). The excess electrons left with the removal of the O atom are distributed in the first two layers with certain (a considerable) fraction filling the Ce-4f states.     

Subluminal to superluminal light propagation in a V-type three-level atomic system interacting with squeezed vacuum

We study the light propagation properties in a V-type three-level atomic system interacting with two independent broadband squeezed baths. Using the graphic method, the dependences of the absorption and the dispersion of the system on the coupling field strength, the incoherent pumping field strength and the intensity of the squeezed vacuum are analysed. The result shows that the probe pulse propagation can be changed from subluminal to superluminal speed.