The overload phenomenon in gas chromatography

The usual concepts of the dynamics of an overloaded solute band fail to explain several phenomena such as the typical “leading-tail” shape and retention deviations exhibited by overloaded peaks, and why these defects are more commonly observed in short columns. These and other related deviations from theory can be rationalized by a non-classical approach to the overloading phenomenon.     

Minimal Length Elements of Thompson's Group F

Elements of the group are represented by pairs of binary trees and the structure of the trees gives insight into the properties of the elements of the group. The review section presents this representation and reviews the known relationship between elements of F and binary trees. In the main section we give a method of determining the minimal lengths of elements of Thompson's group F in the two generator presentation

Generalized Bicyclic Semigroups and Jones Semigroups

In this paper, we consider the generalized bicyclic semigroups B_n = a, b | aⁿb = 1 and the Jones semigroups A_n = a, b | aⁿ⁺¹b = a. They are the generalizations of the bicyclic semigroup B = a, b | ab = 1 and its analogous semigroup A = a, b | a²b = a discovered by P.R., Jones in 1987. The word problem for these kinds of semigroups is solved. It is proved that, for n 2, B_n are bisimple right inverse but not inverse semigroups and that the semigroup C = a, b | a²b = a, ab² = b is the smallest idempotent-free homomorphic image of A_n. Moreover, we also prove that A_n and A_m are mutually embeddable but not isomorphic with each other if n m. As a consequence, different kind of -nontrivial [0-]simple semigroups without idempotents are discussed.AMS 1991 Subject Classification: primary 20M10 secondary 20M05.Supported by NNSF of China (19671063) and KSRF of Sichuan Education Committee ([1999]127).     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees I

Let G be a solvable group with five character degrees. We show that the derived length of G is at most 5. This verifies that the Taketa inequality, dl(G)|cd(G)|, is valid for solvable groups with at most five character degrees.     

The Ground State Energy of a Dilute Two-Dimensional Bose Gas

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E₀/N=(2²/m)|ln(a²)|^–1, to leading order, with a relative error at most O(|ln(a²)|^–1/5). Here N is the number of particles, =N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E₀ is not simply N(N–1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger.     

Calculation of transport parameters in KT-1 tokamak edge plasma

The radial profiles of KT-1 tokamak (major radius of 27 cm, minor radius of 4.25 cm, two poloidal stainless-steel limiters) edge plasma parameters are measured using single and triple electric probes. The particle transport parameters are calculated from the measured edge plasma parameters, and the results are analyzed by the simple fluid approximations. The cross-field particle diffusion coefficient (D) in the boundary plasma of the KT-1 is calculated from the density scrape-off length (λ_n) measured by using a triple probe. The particle density and electron temperature fall exponentially in the radial direction with the e-folding length of λ_n=0.13 cm and λ_e=0.41 cm, respectively. From the scrape-off layer (SOL) model, the experimental values of scrape-off length (λ_n) is used to calculate the cross-field diffusion coefficient (D=1.2×10³cm²/s), roughly corresponding to one third of the typical Bohm value. A simple SOL model with the contribution of recombination is introduced to evaluate the Bohm diffusion in the KT-1 tokamak edge plasma. Cross-field heat conductivity calculated from these deduced values is 5.2D in the SOL of KT-1 edge plasma. These results provide the finally certain information for edge particle transport in the KT-1 boundary plasmas.     

On Unimodular Rows over Polynomial Rings

Let A be a commutative ring and n 3 a positive integer. In this paper, we consider unimodular rows (f₁(x),..., f_n(x)) over A[x]. We prove that, if the row of the leading coefficients of f_i(x) is unimodular over A and a A, then there exists E_n(A[x]) such that (f₁(x),...,f_n(x)) = (f₁(a),...,f_n(a)). Also, if A is a Noetherian ring with finite Krull dimension and the row of leading coefficients satisfies the same condition, then we give a bound for the length of in terms of elementary transvections.Partially supported by INTAS 93–436EXT and DFG–RFBR grant No. 96–01–00092G.2000 Mathematics Subject Classification: 19A13, 19B14, 13C10, 13B25, 13F20     

Existence and uniqueness of rectilinear slit maps

We consider a generalization of the parallel slit uniformization in which the angle of inclination of each image slit is assigned independently. Koebe proved that for domains of finite connectivity there is, up to a normalization, a unique rectilinear slit map achieving any given angle assignment. Koebe's theorem is partially extended to domains of infinite connectivity. A uniqueness result is shown for domains of countable connectivity and arbitrary angle assignments, and an existence result is proved for arbitrary domains under the assumption that the angle assignment is continuous and has finite range. In order to prove the existence result a new extremal length tool, called the crossing-module, is introduced. The crossing-module allows greater freedom in the family of admissible arcs than the classical module. Several results known for the module are extended to the crossing-module. A generalization of Jenkins' module condition for the parallel slit problem is given for the rectilinear slit problem in terms of the crossing-module and it is shown that rectilinear slit maps satisfying this crossing-module condition exist.

     

基于数字图像处理方法的焦距测量技术研究

介绍了基于数字图像处理方法测量透镜焦距的玻罗板分划线快速自动甄别法。该图像处理方法鲁棒性好,采用Canny法进行分划线边缘检测。用重心法计算所有线条的重心,从重心往两边搜索线条,判断选取间隔大的刻划线对,可以提高测量精度。实验数据表明该方法的相对测量不确定度能达到8.5×10-4。为实现以数字图象处理为基础的焦距客观测量提供了一种可行的技术途径。     

小角X射线散射应用研究若干进展

文章从小角X射线散射（small-ande X-ray scattering，SAXS）的理论分析出发，结合国内外SAXS理论和应用研究的最新动态，总结了文章作者所在的研究小组近年来在SAXS技术用于材料微结构表征方面的研究成果。主要包括以下三个方面的内容：（1）有机／无机杂化材料中电子密度波动的研究；（2）弦长度分布函数材料的周期结构的研究；（3）纳米粉末晶化过程的研究。