偏最小二乘法用于同步荧光法同时测定维生素B1,维生素B2和维生素B6

本文将偏最小二乘法结合同步荧光扫描技术对含维生素Ｂ１，Ｂ２和Ｂ６的混合物进行了同时测定。对同步荧光法的测定条件及△λ的选择进行了试验和讨论，比较了△λ分别为６５ｎｍ和３０ｎｍ时的计算结果。所建立的方法用于复合维生素Ｂ片等药片叶Ｂ１，Ｂ２和Ｂ６孤同时测定，获较满意的结果。     

Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.     

Cycle Range Distributions for Gaussian Processes Exact and Approximative Results

Wave cycles, i.e. pairs of local maxima and minima, play an important role in many engineering fields. Many cycle definitions are used for specific purposes, such as crest–trough cycles in wave studies in ocean engineering and rainflow cycles for fatigue life predicition in mechanical engineering. The simplest cycle, that of a pair of local maximum and the following local minimum is also of interest as a basis for the study of more complicated cycles. This paper presents and illustrates modern computational tools for the analysis of different cycle distributions for stationary Gaussian processes with general spectrum. It is shown that numerically exact but slow methods will produce distributions in almost complete agreement with simulated data, but also that approximate and quick methods work well in most cases. Of special interest is the dependence relation between the cycle average and the cycle range for the simple maximum–minimum cycle and its implication for the range distribution. It is observed that for a Gaussian process with rectangular box spectrum, these quantities are almost independent and that the range is not far from a Rayleigh distribution. It will also be shown that had there been a Gaussian process where exact independence hold then the range would have had an exact Rayleigh distribution. Unfortunately no such Gaussian process exists.This revised version was published online in March 2005 with corrections to the cover date.     

Two optimization problems in linear regression with interval data

We consider a linear regression model where neither regressors nor the dependent variable is observable; only intervals are available which are assumed to cover the unobservable data points. Our task is to compute tight bounds for the residual errors of minimum-norm estimators of regression parameters with various norms (corresponding to least absolute deviations (LAD), ordinary least squares (OLS), generalized least squares (GLS) and Chebyshev approximation). The computation of the error bounds can be formulated as a pair of max–min and min–min box-constrained optimization problems. We give a detailed complexity-theoretic analysis of them. First, we prove that they are NP-hard in general. Then, further analysis explains the sources of NP-hardness. We investigate three restrictions when the problem is solvable in polynomial time: the case when the parameter space is known apriori to be restricted into a particular orthant, the case when the regression model has a fixed number of regression parameters, and the case when only the dependent variable is observed with errors. We propose a method, called orthant decomposition of the parameter space, which is the main tool for obtaining polynomial-time computability results.     

Extensions of the prudence principle to exploit a valued outranking relation

In many outranking methods, the alternatives are first compared pairwise to build a valued outranking relation, which is then exploited to derive a recommendation for the decision maker. This paper proposes extensions of Arrow and Raynaud’s prudence principle to exploit a valued outranking relation, even in cases where the outranking values have an ordinal interpretation. The idea is to build a ranking that maximizes the weakest support for its implicit pairwise comparisons. We present a family of exploitation models providing three types of solutions, depending on the decision maker’s request: a linear order, a weak order, or a partial preorder. An algorithm is provided which solves the exploitation models. Relations between these models and some of their properties are also discussed.     

On the system of anisotropic discrete BVPs

We investigate the existence of solutions of the system of anisotropic discrete boundary value problems using critical point theory. We apply direct variational approach, the Ky Fan min–max inequality and the mountain pass lemma.