Analysisin Theory and Applications

Aims and Scope:Analysis in Theory and Applications(ATA)began its publication in 1984.It publishes original papers in the following fields:Approximation Theory,Dynamical Systems,Function Spaces,Fractals,Partial Differential Equations,Geometric Analysis,Harmonic Analysis,Signal Analysis,Transform Analysis,Numerical Approximation,Special Functions     

Association measures for interval variables

Advances in Data Analysis and Classification - Symbolic Data Analysis (SDA) is a relatively new field of statistics that extends conventional data analysis by taking into account intrinsic data...     

DEA-discriminant analysis in the view of goal programming

This article identifies differences and similarities between DEA (Data Envelopment Analysis) and DA (Discriminant Analysis) in the view of GP (Goal Programming). Based upon such characterization, this article proposes a new type of DA technique, referred to as “DEA-Discriminant Analysis (DEA-DA)”, that incorporates a methodological strength of DEA into the DA formulation. This research applies the proposed DEA-DA method to both an illustrative data set and a real case study related to Japanese banks. The importance of DEA-DA is confirmed by comparing it with other DA methods.     

Two-sided stability and convergence of multistage and multistep methods for ordinary differential equations

A norm is introduced which allows the extension of bistability and biconvergence results of Stummel (“Topics in Numerical Analysis, II,” Academic Press, New York, 1975; “Approximation Methods in Analysis,” Aarhus Universiteit, 1973) (which apply to one-step methods) to the case of multistage and multistep methods.     

A Discussion on Variational Analysis in Derivative-Free Optimization

Variational Analysis studies mathematical objects under small variations. With regards to optimization, these objects are typified by representations of first-order or second-order information (gradients, subgradients, Hessians, etc). On the other hand, Derivative-Free Optimization studies algorithms for continuous optimization that do not use first-order information. As such, researchers might conclude that Variational Analysis plays a limited role in Derivative-Free Optimization research. In this paper we argue the contrary by showing that many successful DFO algorithms rely heavily on tools and results from Variational Analysis.

     

Strategic groups based on marginal rates: An application to the Spanish banking industry

This paper uses Data Envelopment Analysis (DEA) to identify strategic groups (SGs) in the Spanish banking industry. The concept of SG relies on the fact that firms grouped together value inputs and outputs in the same way. As such, they take identical direction when, due to external influences, changes are required. Weights obtained from DEA are extremely useful in the valuation of inputs and outputs. Specifically, by comparing DEA weights pair-wise, i.e. quantifying the variables’ marginal rates (MR), we can obtain a very good representation of the existent trade-off and the relative importance of the two variables.The paper uses MRs obtained through DEA models and, simultaneously, proposes feasible ways to overcome two usual problems with DEA virtual weights, namely: (1) the multiplicity of weights for efficient DMUs; and (2) the inexistence of dual variables for inefficient DMUs.From the empirical point of view, once the MRs are determined, the second stage is to perform Cluster Analysis. We apply Cluster Analysis in two ways: (1) on the basis of the MRs; and (2) following the traditional application by running Cluster Analysis with the original variables. The results obtained show the advantages of using MRs instead of the standard application of Cluster Analysis.Summing up, the concept of SG is reinforced if we use refined methods to determine the existence of SGs. The results of the application of DEA models to observe the presence of SG in the Spanish banking industry offer interesting views on it.     

The use of goal programming and data envelopment analysis for estimating efficient marginal costs of outputs

The paper concerns the use of alternative and/or combined methodologies (Data Envelopment Analysis, Regression Analysis, Goal Programming) as a means of ascertaining the efficiency as well as the efficient marginal costs of outputs of homogeneous organizational units. The same body of data is used throughout the analysis and the results derived from the combination of Data Envelopment Analysis and Goal Programming are shown to be more reliable than those obtained by the other methods.     

湖南省各地市州居民生活水平比较分析

本文结合恩格尔系数研究居民生活水平的优点，采用聚类分析法与主成分分析法对2004年湖南省各地市州居民生活水平进行比较分析，给出了这些城市居民生活水平的综合得分及其排序，从而更真实地衡量湖南省各地市州居民生活水平．     

Predicting performance in a first engineering calculus course: implications for interventions

At the University of Louisville, a large, urban institution in the south-east United States, undergraduate engineering students take their mathematics courses from the school of engineering. In the fall of their freshman year, engineering students take Engineering Analysis I, a calculus-based engineering analysis course. After the first two weeks of the semester, many students end up leaving Engineering Analysis I and moving to a mathematics intervention course. In an effort to retain more students in Engineering Analysis I, the department collaborated with university academic support services to create a summer intervention programme. Students were targeted for the summer programme based on their score on an algebra readiness exam (ARE). In a previous study, the ARE scores were found to be a significant predictor of retention and performance in Engineering Analysis I. This study continues that work, analysing data from students who entered the engineering school in the fall of 2012. The predictive validity of the ARE was verified, and a hierarchical linear regression model was created using math American College Testing (ACT) scores, ARE scores, summer intervention participation, and several metacognitive and motivational factors as measured by subscales of the Motivated Strategies for Learning Questionnaire. In the regression model, ARE score explained an additional 5.1% of the variation in exam performance in Engineering Analysis I beyond math ACT score. Students took the ARE before and after the summer interventions and scores were significantly higher following the intervention. However, intervention participants nonetheless had lower exam scores in Engineering Analysis I. The following factors related to motivation and learning strategies were found to significantly predict exam scores in Engineering Analysis I: time and study environment management, internal goal orientation, and test anxiety. The adjusted R² for the full model was 0.42, meaning that the model could explain 42% of the variation in Engineering Analysis I exam scores.     

GAMM Annual Meeting – Luxembourg 2005 Overview of the Sessions

Volume 5 (2005) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the GAMM Annual Meeting 2005, held 28 March–01 April 2005 in Luxembourg. The contributions are grouped according to the minisymposia and sessions of the conference. Minisymposia M1 Water Waves M2 Procedures and Applications of Stochastic Optimization in Traffic Engineering M3 Levelset methods M4 Inverse Problems, Parameter Estimation M5 Multifield Problems M6 Computational Methods in Limit Load and Shakedown Analysis M7 Soft Tissue Biomechanics M8 Structure Dynamics and Transport in Soils Young researchers' Minisymposia (Nachwuchssymposien) N1 Computational Optimisation with Differential Equations N2 Computational Inverse Problems N3 Rolling Contact Mechanics N4 Microstructure in Extended Continua: Modeling and Analysis for Solids Sessions 1–25 1 Linear and Nonlinear Oscillations 2 Stability and Control Theory 3 Multibody Systems and Kinematics 4 Elasticity and Viscoelasticity 5 Plasticity 6 Theory of Materials 7 Damage and Fracture 8 Computational Solid Mechanics 9 Computational Fluid Mechanics 10 Experimental Methods and Identification 11 Gas Dynamics and Rarefield Gases 12 Viscous Flows 13 Transition and Turbulence 14 Heat and Mass Transfer, Convective Flows 15 Multiphase Flows, Flows of Reactive Fluids 16 Waves, Acoustics 17 Applied Analysis 18 Mathematical Methods of the Natural and Engineering Sciences 19 Computer Algebra and Computer Analysis 20 Applied Stochastics, Operations Research 21 Optimisation 22 Numerical Analysis 23 Applied and Numerical Linear Algebra 24 Numerical Treatment of Ordinary and Differential-Algebro Equations 25 Numerical Treatment of Partial Differential Equations     

数学建模在多元统计分析教学中的应用

本利用数学建模的思想对多元统计分析特别是主成分分析方法的教学进行改革，通过使用统计软件SPSS进行计算和分析，使学生对十分抽象的统计概念和深奥的多元统计理论有直现的认识和理解，为掌握多元统计分析方法提供了较好的手段。     

Linear relative canonical analysis of Euclidean random variables,asymptotic study and some applications

We introduce the Linear Relative Canonical Analysis (LRCA) of Euclidean random variables. Then similar properties than for usual linear Canonical Analysis are obtained. Furthermore, we develop an asymptotic study of LRCA and apply the obtained results to tests for lack of relative linear association, dimensionality and invariance.     

Maximum Principle of Optimal Control of the Primitive Equations of the Ocean With State Constraint

We investigate in this paper Pontryagin's maximum principle for a class of control problems associated with the primitive equations (PEs) of the ocean. These optimal problems involve a state constraint similar to that considered in Wang and Wang (Nonlinear Analysis 2003; 52:1911–1931) for the three-dimensional Navier–Stokes (NS) equations. The main difference between this work and Wang and Wang (Nonlinear Analysis 2003; 52:1911–1931) is that the nonlinearity in the PEs is stronger than in the three-dimensional NS systems.     

多元统计分析在医院管理中的应用

本文应用多元统计分析中的聚类分析和因子分析法 ,对辽宁省金秋医院内科循环病房 1997- 1999年的月报表进行了综合评价 ,借以说明多元统计分析用于医院管理的实用性与优越性     

基于人因可靠性的建筑工程质量管理模型分析

人因可靠性分析是风险分析理论的重要内容,通过对建筑工人的人因可靠性分析,建立了建筑工人人因可靠性数学模型,阐述了人因可靠性对建筑工程质量的影响.为工程管理方提高工程管理水平,避免人为差错影响工程质量提供参考.     

Burkholder Inequalities in Riesz spaces

In this paper, the extent to which the Burkholder Inequalities in classical Stochastic Analysis can be generalized to the new Theory of Stochastic Analysis in Riesz spaces.     

On the pathwise computation of derivatives with respect to the rate of a point process: The phantom RPA method

The Rare Perturbation Analysis (RPA) method is presented using two approaches: a direct one and an indirect one via a pathwise interpretation of the Likelihood Ratio Method (LRM). These two approaches give a new point of view for the Smoothed Perturbation Analysis (SPA) discussed in Gong [4] and extend the validity of the formulas therein, in particular to the estimation of derivatives of quantities that can be computed over a busy cycle. A heuristic comparison with LRM is given and simulation results are presented to compare the performance of LRM, RPA, and a finite difference RPA in a simple system.     

Verbal ordinal classification with multicriteria decision aiding

Professionals in neuropsychology usually perform diagnoses of patients’ behaviour in a verbal rather than in a numerical form. This fact generates interest in decision support systems that process verbal data. It also motivates us to develop methods for the classification of such data. In this paper, we describe ways of aiding classification of a discrete set of objects, evaluated on set of criteria that may have verbal estimations, into ordered decision classes. In some situations, there is no explicit additional information available, while in others it is possible to order the criteria lexicographically. We consider both of these cases. The proposed Dichotomic Classification (DC) method is based on the principles of Verbal Decision Analysis (VDA). Verbal Decision Analysis methods are especially helpful when verbal data, in criteria values, are to be handled. When compared to the previously developed Verbal Decision Analysis classification methods, Dichotomic Classification method performs better on the same data sets and is able to cope with larger sizes of the object sets to be classified. We present an interactive classification procedure, estimate the effectiveness and computational complexity of the new method and compare it to one of the previously developed Verbal Decision Analysis methods. The developed and studied methods are implemented in the framework of a decision support system, and the results of testing on artificial sets of data are reported.     

A combined use of DEA (Data Envelopment Analysis) with Strong Complementary Slackness Condition and DEA–DA (Discriminant Analysis)

This study discusses a combined use of DEA (Data Environment Analysis) with SCSC (Strong Complementary Slackness Condition) and DEA–DA (Discriminant Analysis). Many studies use DEA to evaluate the performance of various organizations in private and public sectors. A conventional use of DEA is not perfect because it still contains zero in many multipliers. This implies that DEA does not fully utilize information on all inputs and outputs. As a result, DEA produces many efficient organizations. To overcome the methodological difficulty, this study proposes a new use of DEA/SCSC and DEA–DA to reduce the number of efficient organizations.