On the second eigenfunctions of the Laplacian in R2

A conjecture about the nodal line of a second eigenfunction states that the nodal line of a second eigenfunction divides the domain by intersecting with the boundary of transversely, where is a bounded convex domain ofR ². We prove this conjecture provided has a symmetry. Also, we prove the multiplicity of the second eigenvalue is two at most provided is a bounded convex domain ofR ².Supported in part by NSF DMS 84-09447Home Institution: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA     

A new phenomenological potential for heavy quarkonium

We suggest a new phenomenological potential for heavy quarkonium. The potential has a Lorentz vector term motivated by experimental leptonic widths for vector mesons and perturbative QCD at short distances and a Lorentz scalar term responsible for quark confinement at large distances. Using this potential we calculate the energy levels, leptonic decay widths, radiative transition rates and hadronic decay rates of the \(c\bar c, b\bar b\) and \(t\bar t\) systems. Most results agree well with the experiment.     

渗透蒸发脱盐的研究

将选择性透过膜和汽化相结合的分离过程是当前的研究热点,其中采用低热导率、疏水性多孔膜的过程称膜蒸馏,而采用非多孔性半透膜的过程则称渗透蒸发。将该分离过程用于盐水脱盐已有很多报道,并已建成中试设备,但采用的大多是膜蒸馏,所用膜的成本很高。本文研究制了一种价廉并带有致密层的非对称性含钠离子聚乙烯醇(PVA)-聚乙二醇(PEG)分离膜,并用该膜对渗透蒸发脱盐进行了初步研究。 1 实验 1.1 膜制备 将一定配比的PVA与PEG及钠盐水溶液在适当温度下混溶,加入适量醛类交联剂,数分钟后在选定的基材上流涎成膜,室温下自然晾干,再经35℃～50℃控温红外线干燥。 1.2 膜结构及脱盐流程 扫描电镜拍摄的膜断面形貌图像(图1)表明,该膜为非对称膜,表层厚约13μm,其中厚约2～3/μm的上表层为疏松结构,下表层为致密结构。将该类膜用于3.5％NaCl水溶液脱盐,运行4h后再漂洗、干燥作断面Na元素波谱线分析(图2)发现,在膜下层(右侧)厚约30μm层内检测不到Na元素。脱盐流程见文献。     

L—氨基酸氧化酶电极的制作及电极特性的研究

报道了一种新的Ｌ－氨基酸氧化酶电极，这种酶电极系由氨气敏电极和以氨基化玻璃布为载体的酶膜所组成；研究了固定化条件对酶膜活性的影响以及底物浓度、温度和ｐＨ对电极响应特性的影响。该电极在６．０×１０＾－５～４．０×１０＾－３ｍｏｌ／Ｌ的底物浓度范围内呈良好的线性关系，检测下限为５．０×１０＾－５ｍｏｌ／Ｌ。在最宜条件下，酶电极具有良好的稳定性。     

A remark on H1 mappings

With , we here construct, for each positive integer N, a smooth function of degree zero so that there must be at least N singular points for any map that minimizes the energy in the family . The infimum of over U(g) is strictly smaller than the infimum of over the continuous functions in U(g). There are some generalizations to higher dimensions.Research partially supported by the National Science FoundationResearch supported by an Alfred P. Sloan Graduate Fellowship     

A new method for determination of uric acid by the lactic acid-acetone-BrO(3)(-)-Mn(2+)-H(2)SO(4) oscillating reaction using the analyte pulse perturbation technique

A new analytical method for the determination of uric acid (UA) by the perturbation of UA on the Belousov-Zhabotinsky oscillating reaction is proposed. The method is based on the linear relationship between the changes in the oscillating period and the concentration of UA. The calibration curve is linear over the range of 2.0 × 10⁻⁵ to 5.0 × 10⁻⁴ M, with a detecting limit of 3.28 × 10⁻⁶ M. The method features good precision (R.S.D.: 3.59%) and excellent throughput (10 samples h⁻¹). The possible mechanism of the perturbation of UA on the oscillating reaction is discussed.     

Discovery of High-Pressure Basic Granulite Terrain in North China Archaean Craton and Preliminary Study

High-pressure basic granulite terrain of 2.65 Ga from Jiouhuai'an in the junction of the Hebei and Shanxi provinces was discovered and reported recently. The three metamorphic mineral assemblages and their mineral reaction texture of the basic granulites have been identified, which represent three main metamorphic episodes of 1.4—1.5 Gpa, 800℃; 0.7—0.9 Gpa, 820℃ and 0.5—0.6 Gpa, 700℃. Their steep decompressional clockwise P-T path implies that a late Archaean continental collision and sole thrusting event perhaps occurred in North China Craton. This is important to study petrogenesis of high-pressure granulites, composition and texture of deep crust in North China Craton, and early Precambrian collision tectonism.     

WHOLLY-AROMATIC THERMOTROPIC LIQUID CRYSTALLINE POLYMER AND ITS BLOCK COPOLYMER

A wholly-aromatic thermotropic liquid crystalline polymer (WATLCP) composed ofp-hydroxybenzoic acid (HBA), 4,4'-dihydroxy bisphenyl (BP), terephthalic acid (TPA),m-phthalic acid (MPA) was synthesized. It was symbolized by BP-LCP. Using a simi-lar method, a new copolymer BP-PSF was prepared. BP-PSF has a semi-flexible chainpolysulfone and a rigid-rod chain like BP-LCP. By FT-IR, polarizing microscope and DSCtechnique, the structures and properties of BP-LCP and BP-PSF were studied.