流动注射萃取火焰原子吸收光谱法测定硫酸镍电解液中微量铅

本文采用流动注射在线萃取火焰原子吸收光谱法测定硫酸电解液中微量铅，考察了水相介质，共存离子，萃取装置，相比等因素的影响。分析含铅１．４ｍｇ／Ｌ和０．１６ｍｇ／Ｌ的试样，分析值的相对标准偏差（ｎ＝１０）分别为３．９％和１２．３％，方法检出限为０．０２４ｍｇ／Ｌ。     

Circular Chromatic Indices of Regular Graphs

The circular chromatic index of a graph G, written line.com/cms/attachment/b8eced28-3674-452f-b3c6-e6a917170b57/jgt21757-math-0001.png">, is the minimum r permitting a function line.com/cms/attachment/95e8c4ae-4174-4aa3-ab75-2e177b840f78/jgt21757-math-0002.png"> such that line.com/cms/attachment/9f8bd726-1652-448b-aaa1-d9115e4bd25a/jgt21757-math-0003.png"> whenever e and line.com/cms/attachment/7f512663-e72b-4796-960a-41efb576af13/jgt21757-math-0004.png"> are adjacent. It is known that for any line.com/cms/attachment/abaefd28-623e-4fdc-adfc-57d40c1ad4dd/jgt21757-math-0005.png">, there is a 3‐regular simple graph G with line.com/cms/attachment/f56de7d1-60f2-488f-8ba9-c2ff871d296c/jgt21757-math-0006.png">. This article proves the following results: Assume line.com/cms/attachment/28d005c4-c98e-47d5-9d4a-795f06ec67b7/jgt21757-math-0007.png"> is an odd integer. For any line.com/cms/attachment/149c88f5-aabb-442d-b873-530921dd09b1/jgt21757-math-0008.png">, there is an n‐regular simple graph G with line.com/cms/attachment/c40ab64a-9b71-4989-a982-3e936383f1b9/jgt21757-math-0009.png">. For any line.com/cms/attachment/850532a2-c9b0-464b-8254-525e1a4adc2e/jgt21757-math-0010.png">, there is an n‐regular multigraph G with line.com/cms/attachment/d614ebc5-4369-41fb-8df1-420aed570920/jgt21757-math-0011.png">.     

Spectrum created by line defects in periodic structures

We study a Helmholtz‐type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a three‐dimensional periodic medium; the defect is infinitely extended in one direction, but compactly supported in the remaining two. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. We will show that even small perturbations lead to additional spectrum in the spectral gaps of the unperturbed operator and investigate some properties of the spectrum that is created.     

Enhanced multi-Hoffmann heuristic for efficiently solving real-world assembly line balancing problems in automotive industry

In production systems of automobile manufacturers, multi-variant products are assembled on paced final assembly lines. The assignment of operations to workplaces and workers deter mines the productivity of the manufacturing process. In research, various exact and heuristic solution procedures have been developed for different versions of the so-called assembly line balancing problem.     

求解非线性互补问题的一类光滑Broyden-like方法

非线性互补问题可以等价地转换为光滑方程组来求解. 基于一种新的非单调线搜索准则, 提出了求解非线性互补问题等价光滑方程组的一类新的非单调光滑 Broyden-like 算法.在适当的假设条件下, 证明了该算法的全局收敛性与局部超线性收敛性. 数值实验表明所提出的算法是有效的.     

用高中数学求解异面直线公垂线方程

用高中向量基础知识和待定法可非常方便地得出n（n≥3）维线性空间中异面直线的公垂线方程.若在大学数学教学中挖掘与中学数学的衔接和联系,则可在很大程度上降低大学数学的教学难度.     

带参数共轭梯度法簇的全局收敛性

共轭梯度法是最优化中最常用的方法之一,广泛地应用于求解大规模优化问题,其中参数β_k的不同选取可以构成不同的共轭梯度法.给出了一类含有三个参数的共轭梯度算法,这种算法能够在给定的条件下证明选定的β_k在每一步都能产生一个下降方向,同时在强Wolfe线搜索下,这种算法具有全局收敛性.     

L（1, 2）-edge-labelings for lattices

For a graph G and two positive integers j and k, an m-L(j, k)-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by kThe λ j,k-number of G is the minimum m such that an m-L(j, k)-edge-labeling is admitted by GIn this article, the L(1, 2)-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λ j,k-numbers of these graphs are obtained.     

An Inexact PRP Conjugate Gradient Method for Symmetric Nonlinear Equations

In this article, without computing exact gradient and Jacobian, we proposed a derivative-free Polak-Ribière-Polyak (PRP) method for solving nonlinear equations whose Jacobian is symmetric. This method is a generalization of the classical PRP method for unconstrained optimization problems. By utilizing the symmetric structure of the system sufficiently, we prove global convergence of the proposed method with some backtracking type line search under suitable assumptions. Moreover, we extend the proposed method to nonsmooth equations by adopting the smoothing technique. We also report some numerical results to show its efficiency.