A compact finite difference method for solving Burgers' equation

In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

反射式表面粗糙度光纤传感器及其模糊算法

本文提出了一种新型表面粗糙度光纤传感器,阐述了它的结构、工作原理,给出了测试结果.运用模糊算法,分析实测数据,得到系统的测量规则和隶属函数.经过模糊推理和决策计算出相应的输出值.该算法可减小测量误差,提高测量精度,扩大测量范围.本系统能准确地识别R_a分别为0.012μm,0.025μm,0.5μm,0.1μm的被测表面.     

L(φ,μ)-平均域及其几何特征

本文首先引入L(,μ)-平均域,它是已知的John-域,Ls-平均域和Ls(μ)-平均域等的推广.然后利用拟双曲度量来刻画L(,μ)-平均域的几何特征.最后证明,对于任何满足L(,μ)-平均域定义中条件的函数,John-域是L(,μ)-平均域.     

Recent advances in two-photon imaging: technology developments and biomedical applications

In the past two decades, two-photon microscopy (TPM) transforms biomedicalresearch, allowing nondestructive high-resolution fluorescent molecular imaging and label-free imaging in vivo and in real time. Here we review the recent advances of TPM technologyincluding novel laser sources, new image acquisition paradiams, and microendoscopicimaging systems. Then, we survey the capabilities of TPM imagingof biological relevant molecules such as nicotinamideadenine dinucleotide (NADH), flavin adenine dinucleotide (FAD),and reactive oxygen species (ROS). Biomedical applications of TPM in neuroscience and cancer detection are demonstrated.     

A supramolecular nanovehicle toward systematic,targeted cancer and tumor therapy

A supramolecular nanovehicle (denoted as SNV) was fabricated by encapsulating zinc phthalocyanine (ZnPc) and doxorubicin (DOX) into a copolymer (PVP-b-PAA-g-FA), so as to achieve systematic and synergistic chemotherapy-photodynamic therapy (PDT), targeted tumor imaging and therapy. The sophisticated copolymer designed in this work can load the PDT photosensitizer (ZnPc) and chemotherapy drug (DOX) simultaneously, which exhibits an excellent performance in chemotherapy-PDT targeted cancer and tumor therapy for both in vitro studies performed with HepG2 cells and in vivo tests with mice. This work provides a new drug formulation with a chemotherapy-PDT synergistic effect by virtue of the supramolecular material design, which possesses the advantages of an ultra-low drug dosage and highly-efficient in vivo targeted tumor imaging/therapy.     

Regularization of planar vortices for the incompressible flow

In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations {-?u = λ∑kj=1 B_(δ(x_0,j))(u-κ_j)p+, in ?,u = 0, on ??,where 0 p 1, ? R~2 is a bounded simply-connected smooth domain, κi(i = 1, …, k) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point x0 =(x0,1, …, x0,k) of the Kirchhoff-Routh function defined on ?kcorresponding to(κ1, …, κk), there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as λ→ +∞, the vorticity setcal vorticity strength near each x0,j appr y : uλ κjoaches κj, j = ∩ Bδ(x0,j) shrinks to{x0,j}, and the lo 1, …, k. This result makes the study of the above problem with p ≥ 0 complete since the cases p 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.     

A r (Ω)-Weighted Imbedding Inequalities for A-Harmonic Tensors

We prove the basic A _r ()-weighted imbedding inequalities for A-harmonic tensors. These results can be used to estimate the integrals for A-harmonic tensors and to study the integrability of A-harmonic tensors and the properties of the homotopy operator T: C (D, ^l )C (D, ^l–1).     

接枝环氧树脂/硅溶胶杂化水分散液的制备与表征

利用原位分散法制备了接枝环氧树脂 硅溶胶杂化水分散液 ,并通过红外光谱和 ζ电位测定 ,表征了接枝环氧树脂与硅溶胶之间的杂化作用 .实验结果表明 ,与接枝环氧树脂水分散液相比 ,杂化水分散液的粒径和粘度均减小 .按此探讨了形成杂化水分散液的历程 .初步测定了杂化水分散液成膜后的表面性能 ,发现它们具有更高的硬度和更好的疏水性能 ,与成膜过程中硅溶胶在膜表面的富集效应有关     

The crystal structure of hexabenzoylhexaazaisowurtzitane

The crystal and molecular structure of an interesting cage compound is described. Crystal data: C₄₈H₃₆N₆O₆·(CH₃)₂CO; monoclinic; space group: P2 ₁ /n; a = 14.948(3) Å, b = 15.079(3) Å, c = 19.539(4)Å, = 93.93(3)°, V = 4394(2)ų; and Z = 4.     

Local and global norm comparison theorems for solutions to the nonhomogeneous A-harmonic equation

We establish local and global norm inequalities for solutions of the nonhomogeneous A-harmonic equation A(x,g+du)=h+d^?v for differential forms. As applications of these inequalities, we prove the Sobolev-Poincaré type imbedding theorems and obtain Lp-estimates for the gradient operator ∇ and the homotopy operator T from the Banach space Ls(D,Λl) to the Sobolev space W1,s(D,Λl−1), l=1,2,…,n. These results can be used to study both qualitative and quantitative properties of solutions of the A-harmonic equations and the related differential systems.