Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

ICP－AES法测定金属矿产品中的磷

本文研究了铁矿石、铬矿石、锰矿石中的微量磷的电感耦合等离子体发射光谱法的测定。方法简便，具有很好的精密度和准确度。标准样品的分析结果基本与标称值相吻合，回收率在９５％－１０５％之间。     

溶胶-凝胶制备技术与新型催化材料Ⅲ.溶胶粒子表面修饰方法制备催化膜

提出用溶胶粒子表面修饰方法，结合溶胶凝胶技术制备无机催化膜．该方法的基本原理是利用合适的金属配合物在胶粒表面的吸附作用，经溶胶凝胶过程，将活性组分结合到无机膜中．实验测定结果表明：（ＮｉＥＤＴＡ）２－，ＶＯ－３，ＭｏＯ２－４，（Ｐｄ（ＮＨ３）４）２＋，ＰｄＣｌ２－４，ＰｔＣｌ２－６和ＲｈＣｌ３－６可用来修饰ＡｌＯＯＨ溶胶．以Ｐｄ／γＡｌ２Ｏ３催化膜的制备为例，经三次溶胶凝胶过程，可制得无裂缺的厚度为９μｍ的Ｐｄ／γＡｌ２Ｏ３催化膜，膜材料的平均孔直径为６ｎｍ，Ｐｄ被均匀地分布在膜的顶层，其平均粒径为２３ｎｍ．     

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

对位酚类衍生物作为化学发光分析的增强剂研究

在化学发光分析中，常常要用到碱性条件下鲁米诺与过氧化氢的反应系统，通过催化剂辣根过氧化物酶使反应顺利进行。如果再加入适当的增强剂，则灵敏度提高且发光时间延长，可改善测定的重现性。实验证明，对位酚类衍生物，如：对叔丁基苯酚，对甲苯酚的发光增强作用明显，其发光效率可上升几十倍，发光时间也获得有效延长。     

Diode-pumped 671 nm laser frequency doubled by CPM LBO

A design of diode-pumped high-efficiency Nd:YVO₄/LBO red laser is reported. Using critical phase-matching (CPM) LBO, 671 nm red laser was obtained from 1342 nm light by intracavity frequency doubling. With an incident pump laser of 800 mW, using type-I and type-II CPM LBO, 97 and 52 mWTEM₀₀ mode red laser outputs were obtained, with optical-to-optical conversion efficiencies of up to 12.1% and 6.5%, respectively.     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.     

一种可能的简并谱NNS分布

利用随机矩阵理论,通过对一特殊情形的简并谱展开研究,得到了简并谱一种可能的最小相邻间距NNS分布函数．研究表明,由于简并的存在,简并谱不仅可分解成随机谱和规则谱两个子谱,同时还影响其规则谱,使规则谱的能级斥力减少．