Lower bounds for generalized eigenvalues of the quasilinear systems

In this paper, we establish several new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which generalize or improve all related existing ones. Then we use the Lyapunov-type inequalities obtained in this paper to derive a better lower bound for the generalized eigenvalues of the one-dimensional quasilinear elliptic system with the Dirichlet boundary conditions.     

Applications of antireflection coatings in sonic crystal-based acoustic devices

The unwanted reflection seriously baffles the practical applications of sonic crystals, such as for various acoustic lenses designed by utilizing the in-band properties of sonic crystals. Herein we introduce the concept of the antireflection coating into the sonic crystal-based devices. The efficiency of such accessorial structures is demonstrated well by an originally high reflection system. Promising perspectives can be anticipated in extending the antireflection coating layers into more general acoustic applications through a flexible design process.     

金属介电函数的正确运用——以金属纳米球诱导的二能级系统的基态能级移动为例

金属对电磁场的响应包括自由和束缚电荷两部分的贡献,大学物理教学中通常分别用Drude模型和Lorentz模型描述,然而,以上模型所得的介电函数只在一段较窄的频率范围内能与实验数据吻合.因此,在实际科研工作中,当物理量与较宽频率范围内的电磁场响应有关时,原则上介电函数应当采用实验测量值而不能采用模型化的结果.本文以金属纳米球诱导的二能级系统的基态能级移动为例,分别展示采用模型化的介电函数和实验介电函数时,能级移动计算结果的差异.     

多壁碳纳米管表面大黄素印迹材料制备及吸附性能研究

以表面硅烷修饰的碳纳米管为基材,甲基丙烯酸为功能单体,二甲基丙烯酸乙二醇酯为交联剂,采用表面印迹技术成功制备了大黄素印迹复合材料。采用扫描电镜和透射电镜研究该印迹复合材料的形貌,结果表明,在碳纳米管表面接枝了1层稳定的约40nm厚的印迹层。在pH=8.5时,该印迹材料对大黄素具有较大吸附容量和良好选择吸附性能,最大理论吸附量(Qmax)为20.8mg/g。以该印迹材料作为固相萃取吸附剂,在85%乙醇水溶液淋洗和10%乙酸的乙醇溶液洗脱下,可实现对猕猴桃根样品粗提取液中大黄素固相萃取分离富集,回收率达到85%以上。     

Proposal for an unstrained nanoheterolaser generating a mainly TM-polarized radiation

A semiconductor interband laser based on an unstrained one or multiple quantum well nanoheterostructure and generating a mainly TM-polarized radiation is suggested. The latter feature is ensured by a planar waveguide with a special design, in which, due to the plasmon effect, the absorption of TM modes is smaller than that of TE ones. Via developing a two-dimensional distributed Bragg feedback concept such a device can be employed for the creation of powerful sources of monochromatic near-infrared radiation with high-quality output beams formed by a small number of or even only one lateral mode.     

Structure and Antibacterial Activity of 3-(3,4-Dimethoxyphenyl)furan-2(5<Emphasis Type="Italic">H</Emphasis>)-ones

Abstract  

Crystalline hydrate of the title compound (5), C₁₉H₂₆N₂O₅·2(H₂O), was structurally characterized by single crystal X-ray diffraction. It crystallizes in monoclinic system space group P 21/c with a = 7.3987(7) ?, b = 17.8691(16) ?, c = 17.0022(13) ?, β = 112.944(3)°, V = 2070.0(3) ?³, Z = 4, R ₁ = 0.0592, wR ₂ = 0.1016, and T = 298(2) K. The X-ray structure determination revealed that the center furanone ring is nearly coplanar with 3,4-dimethoxybenzene ring, making a dihedral angle of 0.860(69)°. Two kinds of centrosymmetric tetramers characterized by graph-set motifs of R ₇⁸(36) and R ₄⁶(32) are formed through O–H···O, O–H···N and C–H···O hydrogen bonding interactions, which generate a sheet of edge-fused rings parallel to the (011) plane. These sheets are further linked into a three dimensional network by C–H···π interactions. Nine 3-(3,4-dimethoxyphenyl)furan-2(5H)-ones were synthesized and fully characterized by elemental analysis, MS and ¹H NMR. All of them were evaluated for antimicrobial activities against three Gram-positive organisms and a Gram-negative organism, and compound 5 was the most active against Staphylococcus aureus ATCC 25923.     

Homotopy method for a mean curvature-based denoising model

Variational image denoising models based on regularization of gradients have been extensively studied. The total variation model by Rudin, Osher, and Fatemi (1992) [38] can preserve edges well but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To overcome this, mean curvature-based energy minimization models offer one approach for restoring both smooth (no edges) and nonsmooth (with edges) images. As such models lead to fourth order (instead of the usual second order) nonlinear partial differential equations, development of fast solvers is a challenging task. Previously stabilized fixed point methods and their associated multigrid methods were developed but the underlying operators must be regularized by a relatively large parameter. In this paper, we first present a fixed point curvature method for solving such equations and then propose a homotopy approach for varying the regularized parameter so that the Newton type method becomes applicable in a predictor-corrector framework. Numerical experiments show that both of our methods are able to maintain all important information in the image, and at the same time to filter out noise.     

Optical multistability and cooling of a micromechanical mirror induced by radiation pressure in optomechanical cavity

The radiation-pressure induces the movable mirror and the steady-state amplitude of the cavity field displaying an optical multistable behavior is investigated in detail by numerical evaluation in Fabry–Perot optical cavity. We introduce an approximation scheme to derive and analyze the final effective mean phonon number using linearized quantum Langevin equation to describe optomechanical cooling. Our results show that the movable mirror can be cooled close to its ground state with low initial temperature and high mechanical quality factor.     

超声波作用下乙酸辛酯合成条件的研究

在超声波作用下,不用溶剂,以硫酸氢钠为催化剂催化合成乙酸辛酯。最佳反应条件是:正辛醇和乙酸的物质的量比为1∶2.0,催化剂用量为反应物总质量的1.0%,超声时间20min,反应温度84℃。在此反应条件下,酯收率可达80.1%,催化剂可重复使用。     

INTEGRAL BOUNDARY VALUE PROBLEM FOR FIRST ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS

By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-differential equations.