Functional Analysis

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H.c.m. Didden - One of the best experts on this subject based on the ideXlab platform.

  • Functional Analysis methodology in developmental disabilities
    2020
    Co-Authors: N.c. Peters-scheffer, H.c.m. Didden
    Abstract:

    Since the first publications more than 40 years ago, the Functional Analysis approach has significantly contributed to improving the lives of individuals with developmental disabilities, including autism. Important gains in both conceptual and applied work have been made in the teaching of adaptive skills and the assessment and remediation of problem behavior. Functional Analysis methodology provides an empirically validated framework for the assessment and treatment of challenging behavior. In this chapter, we describe basic assumptions of this approach, review methods for conducting Functional Analysis in clinical practice, review function-based treatments, and present a brief example of its application.

  • Functional Analysis methodology in developmental disabilities
    Functional Analysis in Clinical Treatment, 2007
    Co-Authors: H.c.m. Didden
    Abstract:

    Publisher Summary This chapter describes the basic assumptions of the Functional Analysis methodology approach. The chapter reviews (1) the methods for conducting Functional Analysis in clinical practice and (2) the function-based treatments. Functional Analysis is a methodology for systematically investigating relationships between problem behavior and environmental events. Its purpose is to identify variables controlling behavior and to generate hypotheses about its functions. It is the function of the behavior, not its topography, that guides treatment selection. A distinction is made between descriptive and experimental methods. Descriptive or nonexperimental methods are also referred to as Functional assessment. Experimental methods or Functional Analysis refers to procedures that systematically manipulate environmental conditions to assess effects on the rates of problem behavior. Descriptive Analysis involves methods of both indirect and direct observation of the target behavior and environmental events. Such methods are typically implemented in naturally occurring applied settings.

G. B. Shpiz - One of the best experts on this subject based on the ideXlab platform.

  • Idempotent Functional Analysis: An algebraic approach
    Mathematical Notes, 2001
    Co-Authors: G. L. Litvinov, Victor Pavlovich Maslov, G. B. Shpiz
    Abstract:

    This paper is devoted to Idempotent Functional Analysis, which is an “abstract” version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a brief survey of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of traditional Functional Analysis and its idempotent version is discussed in the spirit of N. Bohr's correspondence principle in quantum theory. We present an algebraic approach to Idempotent Functional Analysis. Basic notions and results are formulated in algebraic terms; the essential point is that the operation of idempotent addition can be defined for arbitrary infinite sets of summands. We study idempotent analogs of the basic principles of linear Functional Analysis and results on the general form of a linear Functional and scalar products in idempotent spaces.

  • Idempotent Functional Analysis: an algebraic approach
    arXiv: Functional Analysis, 2000
    Co-Authors: G. L. Litvinov, Victor Pavlovich Maslov, G. B. Shpiz
    Abstract:

    In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of the traditional Functional Analysis and its idempotent version is discussed; this correspondence is similar to N. Bohr's correspondence principle in quantum theory. We present an algebraical approach to Idempotent Functional Analysis. Basic notions and results are formulated in algebraical terms; the essential point is that the operation of idempotent addition can be defined for arbitrary infinite sets of summands. We study idempotent analogs of the main theorems of linear Functional Analysis and results concerning the general form of a linear Functional and scalar products in idempotent spaces.

Eberhard Zeidler - One of the best experts on this subject based on the ideXlab platform.

  • Applied Functional Analysis: Applications to Mathematical Physics
    1995
    Co-Authors: Eberhard Zeidler
    Abstract:

    The first part of a self-contained, elementary textbook, combining linear Functional Analysis, nonlinear Functional Analysis, numerical Functional Analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how Functional Analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.

  • Principles of Linear Functional Analysis
    Applied Functional Analysis, 1995
    Co-Authors: Eberhard Zeidler
    Abstract:

    Linear Functional Analysis is based on the following two important principles: (i) the Hahn-Banach theorem, and (ii) the Baire theorem.

G. L. Litvinov - One of the best experts on this subject based on the ideXlab platform.

  • Idempotent Functional Analysis: An algebraic approach
    Mathematical Notes, 2001
    Co-Authors: G. L. Litvinov, Victor Pavlovich Maslov, G. B. Shpiz
    Abstract:

    This paper is devoted to Idempotent Functional Analysis, which is an “abstract” version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a brief survey of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of traditional Functional Analysis and its idempotent version is discussed in the spirit of N. Bohr's correspondence principle in quantum theory. We present an algebraic approach to Idempotent Functional Analysis. Basic notions and results are formulated in algebraic terms; the essential point is that the operation of idempotent addition can be defined for arbitrary infinite sets of summands. We study idempotent analogs of the basic principles of linear Functional Analysis and results on the general form of a linear Functional and scalar products in idempotent spaces.

  • Idempotent Functional Analysis: an algebraic approach
    arXiv: Functional Analysis, 2000
    Co-Authors: G. L. Litvinov, Victor Pavlovich Maslov, G. B. Shpiz
    Abstract:

    In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of the traditional Functional Analysis and its idempotent version is discussed; this correspondence is similar to N. Bohr's correspondence principle in quantum theory. We present an algebraical approach to Idempotent Functional Analysis. Basic notions and results are formulated in algebraical terms; the essential point is that the operation of idempotent addition can be defined for arbitrary infinite sets of summands. We study idempotent analogs of the main theorems of linear Functional Analysis and results concerning the general form of a linear Functional and scalar products in idempotent spaces.

Victoria Carhart - One of the best experts on this subject based on the ideXlab platform.

  • Functional Analysis in Behavioral Medicine
    European Journal of Psychological Assessment, 2011
    Co-Authors: William H. O'brien, Victoria Carhart
    Abstract:

    Behavior therapists must often design treatments for individual patients who present with a wide array of psychophysiological disorders and health problems. The Functional Analysis and Functional analytic causal modeling is a learning-based, empirically focused assessment technique used to systematically gather, integrate, and summarize information about the form and function of a patient’s symptoms. A Functional analytic case model can be a critical component of effective treatment design because most interventions attempt to modify relationships between causal factors and symptoms. The objectives of this paper are (a) to present a review of the conceptual foundations and essential procedures in the Functional Analysis; (b) to outline steps required to generate a Functional analytic causal model; (c) to explain simple decisional and statistical procedures that can be used to counter intuitive errors; and (d) to demonstrate how Functional analytic case models can be used to guide clinical practice and tre...