Aligning retention time shifts in HPLC three‐dimensional spectra by icoshift approach combined with data arrangement methods and the release of a graphical user interface

High‐performance liquid chromatography coupled with photodiode array detection has been extensively applied in many fields and the peaks among the analyzed samples can be shifted due to the variations of instrumental and experimental conditions. In multivariate analysis, retention time alignment is an important pretreatment step. Hence, the shifted peaks in high‐performance liquid chromatography coupled with photodiode array detection three‐dimensional spectra should be aligned for further analysis. Being motivated by this purpose, the interval correlated shifting method combined with the proposed data arrangement methods are recommended and employed on high‐performance liquid chromatography coupled with photodiode array detection data as a demonstration. We validate the alignment performance of the proposed method through comparison the consistency of the retention time before and after alignment. The obtained results demonstrated that the proposed method is capable of successful aligning the employed data. Additionally, the interval correlated shifting method combined with the data arrangement modes is implemented in an easy‐to‐use graphical user interface environment and so can be operated easily by users not familiar with programming languages.     

Multiplicative processes and power laws in human reaction times derived from hyperbolic functions

In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéron?s law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipf?s law are analyzed.     

Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L ²-norm. For the multi-interval spectral method in time, the L ²-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.     

关于区间割线法的有效性

本文我们讨论求凸连续函数的零点的区间割线法 ,所构造的方法简捷、实用 ,且具有较高的收敛效率 (三次函数计值 ,为三阶收敛 ).     

Safe bounds in linear and mixed-integer linear programming

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap pre- and postprocessing of the linear programs arising in a branch-and-cut framework can guarantee that no solution is lost, at least for mixed-integer programs in which all variables can be bounded rigorously by bounds of reasonable size. Mathematics Subject Classification (2000):primary 90C11, secondary 65G20     

Continuity of Effect Algebra Operations in the Interval Topology

We study the continuity of and of effect algebras in the interval topology, and present several examples of effect algebras with interesting properties.     

Real bounds, ergodicity and negative Schwarzian for multimodal maps

We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have `negative Schwarzian derivative' and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow to have inflection points.

     

MULTIFRACTAL FORMALISMS：BOXED VERSUS CENTERED INTERVALS

There are mainly two approaches to the multifractal analysis of measures. The first one, which is used in applications and in studying problems arising from dynamical systems, uses a hierarchy of boxes. The second one, which is more satisfactory from the viewpoint of geometric measure theory, uses more intrinsicconcepts. This article is an account of a work by J. Barral, F. Ben Nasr, and J. Peyriere [3] which pro-vides a bridge between these two theories.     

A Large Sample Approximation to the Profile Plug-in Upper Confidence Limit

We consider the problem of constructing a 1– upper confidence limit for the scalar parameter ₀ in the presence of the nuisance parameter vector ₀, when the data are discrete. The 'profile plug-in' upper confidence limit is introduced by Kabaila and Lloyd. This confidence limit is based on computing a P-value from an estimator of ₀, replacing the nuisance parameter by the profile maximum likelihood estimate for known, and equating to . Theoretical and numerical evidence for the good coverage properties of this confidence limit is presented by Kabaila and Lloyd. An upper confidence limit should be assessed not only by its coverage properties but also by how large this confidence limit is. We measure how large the profile plug-in upper limit is by using a large sample approximation to it. This large sample approximation is used to delineate further the good properties of this confidence limit.     

区间数的排序方法研究

指出献^[3-5]所定义的用于区间数排序的可能度存在的不足,分别给出了刻画区间数大小比较的相对优势度的定义和模糊互补矩阵排序的一种新方法。在此基础上,给出了区间数的一种排序方法。