Invariance principles for hybrid systems with memory

Hybrid systems with memory are dynamical systems exhibiting both delayed and hybrid dynamics. Such systems can be described by hybrid functional inclusions. Classical invariance principles play an instrumental role in proving stability and convergence of dynamical systems. Invariance principles for general hybrid systems with delays, however, remain an open topic. In this paper, we prove invariance principles for hybrid systems with memory, using both Lyapunov–Razumikhin function and Lyapunov–Krasovskii functional methods. These invariance principles are then applied to derive two stability results as corollaries.     

Cu∶CdS纳米晶的绿色合成、结构及光谱性质研究

本文利用一种绿色合成工艺,采用巯基乙酸作为配体,在水溶液中成功合成了水溶性的Cu∶CdS纳米晶。利用X射线衍射分析(XRD)、傅里叶变换红外光谱(FT-IR)、场发射扫描电镜显微分析(FE-SEM)、能量色散X射线谱(EDX)、紫外可见(UV-Vis)吸收光谱对样品的晶体学性质、结构、形貌、成分、吸收光谱性质进行了系统的研究。着重研究了掺杂浓度对Cu∶CdS纳米晶的晶体学性质及吸收光谱的影响。结果表明:合成的Cu∶CdS纳米晶为立方相,通过谢乐公式估算的平均晶粒尺寸约为2 nm;随着掺杂浓度的增加,产物的晶胞参数也逐渐增大,表明Cu离子已经掺入到CdS纳米晶中,该发现与EDX结果相吻合。FT-IR红外光谱发现,配体巯基乙酸成功包覆在纳米晶的表面。UV-vis吸收谱表明,掺杂后的Cu∶CdS纳米晶的吸收峰向长波长方向移动。这种红移主要是Cu离子在CdS纳米晶中的掺杂而形成电子能级跃迁所致。     

Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold $\overline{M}$. We first assume the pull back Weitzenböck operator of $\overline{M}$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of $\overline{M}$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when $\overline{M}$ is the space form.     

Rational Synthesis of Iron/Nitrogen-Doped Carbon Catalyst through a Spatial Isolation Strategy for Efficient Oxygen Reduction in Acidic and Alkaline Media

It remains challenging to rationally synthesize iron/nitrogen-doped carbon (Fe/N-C) catalysts with rich Fe−N_x atomic active sites for improved oxygen reduction reaction (ORR) electrocatalysis. A highly efficient Fe/N-C catalyst, which has been synthesized through a spatial isolation strategy, is reported. Derived from bioinspired polydopamine (PDA)-based hybrid microsphere precursors, it is a multifunctional carrier that loads atomically dispersed Fe³⁺/Zn²⁺ ions through coordination interactions and N-rich melamine through electrostatic attraction and covalent bonding. The Zn²⁺ ions and melamine in the precursor efficiently isolate Fe³⁺ atoms upon pyrolysis to form rich Fe−N_x atomic active sites, and generate abundant micropores during high-temperature treatment; as a consequence, the resultant Fe-N/C catalyst contains rich catalytically active Fe−N_x sites and a hierarchical porous structure. The catalyst exhibits improved ORR activity that is superior to and close to that of Pt/C in alkaline and acidic solutions, respectively.     

Modeling of gravity-induced shape distortions during sintering of cylindrical specimens

A finite element approach for modeling the gravity-affected sintering process is presented. The constitutive equations are based on the continuum theory of sintering in the framework of a linear viscous material behavior. The model describes the gravity influence on porosity evolution and shrinkage inhomogeneity. Simulations of densification, shape distortion, and porosity gradients are presented. The results are compared with a previously developed analytical model of sintering under the influence of gravity. First time a direct assessment of the impact of the densification inhomogeneity on the gravity-induced shape distortion during sintering is provided in a generic form similar to the master sintering curve approach.     

The d-very ampleness of adjoint line bundles on quasi-elliptic surfaces

In this paper, we give a numerical criterion of Reider-type for the d-very ampleness of the adjoint line bundles on quasi-elliptic surfaces, and meanwhile we give a new proof of the vanishing theorem on quasi-elliptic surfaces emailed from Langer and show that it is the optimal version.     

Surface effects in the deformation of an anisotropic elastic material with nano-sized elliptical hole

We examine the effect of surface energy on an anisotropic elastic material weakened by an elliptical hole. A closed-form, full-field solution is derived using the standard Stroh formalism. In particular, explicit expressions for the hoop stress, normal, in-plane tangential and out-of-plane displacement components along the edge of the hole are obtained. These expressions clearly demonstrate the effect of elastic anisotropy of the bulk material on the corresponding field variables. When the material becomes isotropic, the hoop stress agrees with the well-known result in the literature while both the in-plane tangential and out-of-plane displacements vanish and the normal displacement is constant along the entire boundary of the elliptical hole.     

Lagrangian actions for elliptical solutions of 2-body and 3-body problems with fixed energies

Based on the works of Gordon (1977) and Zhang and Zhou (2001) on the variational minimizing properties for Keplerian orbits and Lagrangian solutions of Newtonian 2-body and 3-body problems, we use the constrained variational principle of Ambrosetti and Coti Zelati (1990) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies. We also find an interesting relation between the period and the energy for Lagrangian elliptical solutions with Newtonian potentials.     

Synthesis of 7-Alkoxyquinolines,Coumarins, and Resorufins

Synthesis of the title compounds by treatment of the sodium salts of 7-quinolinol, 7-hydroxycoumarin, and resorufin with alkyl halides is described.     

Fluorescent Carbon Dots as Cost-Effective and Facile Probes for Caffeic Acid Sensing via a Fluorescence Quenching Process

Caffeic acid (CA), a familiar color stabilizing reagent, has aroused general concern due to its uncontrolled addition, and thus the detection of CA is increasingly important. In our report, the bright carbon dots (CDs) were prepared via hydrothermal treatment with urea and citric acid act as raw material and their characteristics were discussed through X-ray diffraction (XRD), transmission electron microscopy (TEM) and so on. Impressively, the strong emission of the as-prepared CDs (Quantum Yield: 24.3%) decreased sharply upon a full reaction with the added CA. Hence, we first present an improved strategy for determining CA based upon the quenching of the strong emission of CDs. In this strategy, 0.79–100.0 µmol L^??1 caffeic acid could be simply detected, and a detection limit of 0.24 µmol L^??1 was allowed. Additionally, CA in red wine samples can be successfully detected by this method and the exploration of the quenching mechanism of the CA-CDs system was done.