二阶Melnikov函数及其应用

在Ｍｅｌｎｉｋｏｖ函数的种种应用中，目前常见到的仅是一阶形式。本文具体推导了二阶Ｍｅｌｎｉｋｏｖ函数的分析表达，提出了临界情况下考察双曲鞍点的稳定流形与不稳定流形相对位置的二阶判据，并成功地用于环面ｖａｎｄｅｒＰｏｌ方程的研究中。     

Algorithms for finding proper essential surfaces in 3-manifolds

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Calculus I: The first derivative of pseudoisotopy theory

Let P be the (stable, smooth) pseudoisotopy space of the space X. For any map Y: YX of spaces, we identify the homotopy type of the fiber of P(f): P(f) P(f) in a stable range, roughly twice the connectivity of the map YX. We establish some language for discussing and manipulating such stable-range relative calculations for any homotopy functor. The theorem about P has a corollary about Waldhausen's A. Dedicated to Alexander GrothendieckResearch supported in part by NSF grant DMS-8806444 and by a Sloan Fellowship. Research at MSRI supported in part by NSF grant DMS-8505550.     

On-line sorption preconcentration of metals based on mixed micelle cloud point extraction prior to their determination with micellar chemiluminescence: Application to the determination of chromium at ng l levels

The on-line incorporation of cloud point extraction (CPE) to flow injection analysis (FIA) is modified to extract and preconcentrate metal species rapidly, avoiding the formation of hydrophobic complexes, using a mixed micellar medium. Coupling the procedure with chemiluminescence (CL) detection based on the catalytic activity of metal species on the luminol-hydrogen peroxide reaction and enhancing the signal with the presence of a micellar carrier containing bromide ions produces a powerful tool for the preconcentration and determination of metal species at ng l⁻¹ levels. As an analytical demonstration ultratrace concentrations of chromium were conveniently detected and quantified in samples with a complex matrix such as seawater and wastewater. The figures of merit for the determination of chromium were: 0.9-1.6% R.S.D. (n=5) with detection and quantification limits 0.5 and 2.0 ng l⁻¹, respectively. The calibration graph was rectilinear from 2 to 200 ng l⁻¹ (r=0.9996, n=6). Several other metal ions were determined in ideal situations, with analogous results.     

含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*

在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|²dx) Δu + λV (x)u = μf(x)|u|^q?2u + |u|^p?2u, x ∈ R³,u ∈ H¹(R³),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到.     

用环形扩散管和滤纸联用采样技术采集空气中氨和铵盐

建立了环形扩散管和滤纸采样夹联用，分形态同时采集空气中所态氨和颗粒态铵盐的方法。在同一气流中，采用涂渍１．５％草酸乙醇水溶液的环形扩散管采集气态氨，用浸渍上述试剂的玻璃纤维纸和慢速定量滤纸分别采集颗粒安和第一层滤纸上的铵盐挥发产生的氨气。用靛酚蓝比色法分别测定氨和铵盐。当采气流速为１．０Ｌ／ｍｉｎ时，采样效率高于９８．２％。将本法测得的氨气和铵盐的总量与标准采样方法的测定结果比较。无显著性差异（Ｐ     

The construction and evaluation of a high pressure manifold and vessels for a Calvet type microcalorimeter

A Setaram C-80 calorimeter has been modified in order to measure the heat flow of energetic materials at pressures up to 69 MPa. A manifold and sample cells capable of operating at high pressure were designed, constructed and evaluated. This paper will describe, in detail, the high pressure manifold construction, safety assessment and calibration. As well, the results for initial trials with ammonium nitrate (AN), and pentaerythritol tetranitrate (PETN) at various pressures and heating rates will be discussed.     

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.     

适用于圆筒形增益区的同轴四镜腔的失调分析

采用矩阵光学方法,对适用于可见光的圆筒形增益区同轴四镜腔中的腔镜因倾斜而产生的失调特性进行了分析,给出了相关计算公式。该四镜腔由同轴的一个复曲面全反镜和两个光学玻璃加工的透镜和一个平面输出镜组成。以He-Ne激光器为例,给出了数值计算结果,关键元件复曲面镜的失调对输出的影响较大。这为腔元件的加工以及腔镜的安装调试提供了参考。