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On equalities of estimations of parametric functions under a general linear model and its restricted models

METRIKA 2010年第3期72卷 313-330页

作者： Tian, Yongge Cent Univ Finance & Econ China Econ & Management Acad Beijing 100081 Peoples R China

Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations of matrices and their generalized inverses. In the past several years, a powerful tool-the matrix rank method was utilized to manipulate various complicated matrix expressions that involve generalized inverses of matrices. In this paper, we use this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted model.

关键词： General linear model Restricted linear model OLSE BLUE parametric functions Estimability Equality of estimations

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Students' reasoning about relationships between variables in a real-world problem

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JOURNAL OF MATHEMATICAL BEHAVIOR 2015年 40卷 192-210页

作者： Stalvey, Harrison E. Vidakovic, Draga Georgia State Univ Dept Math & Stat Atlanta GA 30303 USA

This paper reports on part of an investigation of fifteen second-semester calculus students' understanding of the concept of parametric function. Employing APOS theory as our guiding theoretical perspective, we offer a genetic decomposition for the concept of parametric function, and we explore students' reasoning about an invariant relationship between two quantities varying simultaneously with respect to a third quantity when described in a real-world problem, as such reasoning is important for the study of parametric functions. In particular, we investigate students' reasoning about an adaptation of the popular bottle problem in which they were asked to graph relationships between (a) time and volume of the water, (b) time and height of the water, and (c) volume and height of the water. Our results illustrate that several issues make reasoning about relationships between variables a complex task. Furthermore, our findings indicate that conceiving an invariant relationship, as it relates to the concept of parametric function, is nontrivial, and various complimentary ways of reasoning are favorable for developing such a conception. We conclude by making connections between our results and our genetic decomposition. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Calculus students parametric functions Graphing Bottle problem APOS

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Analysis using higher-order XFEM: implicit representation of geometrical features from a given parametric representation

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MECHANICS & INDUSTRY 2014年第5期15卷 443-448页

作者： Moumnassi, M. Bordas, S. P. A. Figueredo, R. Sansen, P. ESIEE Amiens F-80082 Amiens 2 France Cardiff Univ Sch Engn Inst Mech & Adv Mat Cardiff CF24 3AA S Glam Wales

We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach.

关键词： Higher-order XFEM curved boundary parametric functions implicit boundary representation graded sub-mesh (GSM)

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parametric DECOMPOSITION OF THE SPECTRAL ENVELOPE

PARAMETRIC DECOMPOSITION OF THE SPECTRAL ENVELOPE

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Machado, Anderson Fraiha Bonafonte, Antonio Queiroz, Marcelo Univ Sao Paulo Dept Comp Sci BR-05508 Sao Paulo Brazil Univ Politecn Cataluna Barcelona Spain

ISBN: (纸本)9781479903566

In this paper we propose a novel representation of the spectral envelope of speech, using sums of general parametric basis functions (filter bank), including Gaussian, Hann and Nutall. The central frequency and bandwidth of each filter can be adjusted independently for each speech frame as in conventional filter bank analysis. The quality of the representation has been evaluated with respect to a reference spectral envelope obtained from the Harmonic-Stochastic Model [1] (HSM), and also with respect to parameter time stability and separability of different acoustic classes. Numerical results show that the use of the basis functions proposed is an improvement over pure Gaussian models of the spectral envelope.

关键词： spectral envelope representation spectral decomposition parametric functions speech modeling

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On the equivalence of estimations under a general linear model and its transformed models

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LINEAR ALGEBRA AND ITS APPLICATIONS 2009年第10期430卷 2622-2641页

作者： Tian, Yongge Puntanen, Simo Cent Univ Finance & Econ China Econ & Management Acad Beijing 100081 Peoples R China Univ Tampere Dept Math & Stat FI-33014 Tampere Finland

Some necessary and sufficient conditions are given for two equalities of ordinary least-squares estimators and best linear unbiased estimators of an estimable vector of parametric functions under a general linear mode... 详细信息

关键词： General linear model Transformed model Subsample models Reduced models OLSE BLUE parametric functions Estimability Matrix rank method

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Function-based haptic collaboration in X3D 09

Function-based haptic collaboration in X3D

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Proceedings of the 14th International Conference on 3D Web Technology

作者： Lei Wei Alexei Sourin Herbert Stocker Nanyang Technological University Bitmanagement Software GmbH Germany

ISBN: (纸本)9781605584324

We seek to further expand X3D by augmenting it with function-based definitions of geometry, appearance and tangible physical properties. Besides using alone, the introduced nodes can augment and enrich the standard X3D shapes by function-defined geometry, appearance and tangible physical properties. These new virtual objects can be explored haptically with various desktop force-feedback devices. We also propose a general visual and haptic collaborative framework for using it with X3D. We implement it as new pilot versions of BS Collaborate server and BS Contact VRML/X3D viewer. In our collaborative framework, two pipelines---visual and haptic---complement each other to provide a simple and efficient solution to problems requiring collaboration in shared virtual spaces on the web.

关键词： 3D web visualization X3D function-based shape modeling implicit functions collaborative platform physical properties parametric functions haptic interaction

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Function-based visualization and haptic rendering in shared virtual spaces

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VISUAL COMPUTER 2008年第10期24卷 871-880页

作者： Wei, Lei Sourin, Alexei Sourina, Olga Nanyang Technol Univ Singapore Singapore

We seek to further expand the collaborative potential of shared virtual spaces by using haptic force-feedback. We propose how to define tangible physical properties of the objects, together with their geometry and appearance, by using mathematical functions. We illustrate this concept by developing software which allows us to touch and feel surfaces of VRML and X3D objects, convert them to solid objects, as well as create any other solid objects using the function-based extension of VRML and X3D. We define geometry, appearance and tangible physical properties of the solid objects by implicit, explicit and parametric functions straight in the VRML/X3D code or in loadable libraries. Since the function-defined models are small in size, it is possible to perform their collaborative interactive modifications with concurrent synchronous visualization at each client computer with any required level of detail. We illustrate the proposed models with several application examples.

关键词： web visualization shared virtual environments haptic interaction implicit functions parametric functions

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Function-based visualization and haptic rendering in shared virtual spaces

Function-based visualization and haptic rendering in shared ...

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International Conference on Cyberworlds

作者： Wei, Lei Sourin, Alexei Sourina, Olga Nanyang Technol Univ Singapore Singapore

关键词： web visualization shared virtual environments haptic interaction implicit functions parametric functions

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GA-optimal partially balanced fractional 2^m1+^m2 factorial designs of resolution R({00;10;01}|Ω) with 2 ≤ m₁, m₂ ≤ 4

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HIROSHIMA MATHEMATICAL JOURNAL 2007年第1期37卷 119-143页

作者： Lu, Shujie Taniguchi, Eiji Kuwada, Masahide Hyodo, Yoshifumi Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan Okayama Univ Sci Grad Sch Informat Okayama 7000005 Japan

Under the assumption that the three-factor and higher-order interactions are negligible, we consider a partially balanced fractional 2(m1)+(m2) factorial design derived from a simple partially balanced array such that the general mean, all the m(1) + m(2) main effects, and some linear combinations of m1 2 ((m1)(2)) two-factor interactions, of the m2 2 ((m1)(2)) ones and of the m(1)m(2) ones are estimable, where 2 <= m(k) for k = 1,2. This paper presents optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non-negligible factorial effects, where 2 <= m(1), m(2) <= 4.

关键词： ETMDPB association algebra GA-optimality criterion parametric functions PBFF designs Resolution SPBA

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GA-optimal Partially Balanced Fractional 2(1)(m) (+ m)(2) Factorial Designs of Resolutions R({10,01} boolean OR Omega* | Omega) with 2 <= m(1), m(2) <= 4

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2007年第3-4期1卷 427-464页

作者： Lu, Shujie Taniguchi, Eiji Hyodo, Yoshifumi Kuwada, Masahide Hiroshima Univ Grad Sch Engn Higashihiroshima Japan Okayama Univ Sci Grad Sch Informat Okayama Japan

We consider a partially balanced fractional 2(m1+m2) factorial design derived from a simple partially balanced array such that all the m(1) main effects (= theta(10) , say) and all the 2 m ones ( = theta(01), say) are estimable, and in addition that the general mean ( = theta(00), say) is at least confounded ( or aliased) with the factorial effects of the (m(1)/2) two-factor interactions ( = theta(20), say), the (m(2)/2) ones ( = theta(02), say) and/or the m(1)m(2) ones ( = theta(11), say), where the three-factor and higher-order interactions are assumed to be negligible, and 2 <= m(k) for k = 1,2. Furthermore optimal designs with respect to the generalized A-optimality criterion are presented for2 <= m(1)m(2) <= 4when the number of assemblies is less than the number of non-negligible factorial effects.

关键词： ETMDPB association algebra GA-optimality criterion parametric functions PBFF designs Resolution SPBA

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