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A Comparative Analysis of Functional Correctness
ACM Computing Surveys, 1982Abstract : The functional correctness technique is presented and explained. An implication of the underlying theory for the derivation of loop invariants is discussed. The functional verification conditions concerning program loops are shown to be a specialization of the commonly used inductive assertion verification conditions.
Douglas D. Dunlop, Victor R. Basili
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Implications of functional analysis
British Journal of Clinical Psychology, 1983This brief paper is intended to amplify three points which are contained in Slade (1982) and Owens & Ashcroft (1982). They are that (i) functional relationships must be demonstrated, not merely claimed; (ii) functional relationships are likely to be complex, and clinicians should be wary of superficial analysis; and (iii) there is a distinction ...
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Analysis on Aggregation Function Spaces
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2014In many decision-making problems, different methods usually yield different results. In this paper, we study all possible rankings of alternatives produced by applying a set of aggregation functions on a decision matrix. Those possible rankings depend on the aggregation functions that we use and the structures of the decision matrix.
Zhao Zhang, Zeshui Xu
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Elements of functional analysis
1976Let L be a linear space over a topological field K. Suppose that: 1. L is a topological group under addition; 2. the mapping \( K \times L \to L:\left( {\lambda ,x} \right) \to \lambda x \) is continuous in both variables.
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Functional analysis of measurements
Electrical Engineering, 1946HISTORY tells us that measurement has been one of the principal foundations upon which the material progress of mankind has been based. It is only by carefully comparing or measuring the unknown in terms of some known quantity or unit that real knowledge is advanced.
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Definability in functional analysis
Journal of Symbolic Logic, 1997AbstractThe role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples.We introduce the notion of definable real-valued function in functional analysis: a real-valued function f defined on a structure of functional analysis is definable
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The Shaping of Functional Analysis
Bulletin of the London Mathematical Society, 1997This paper (based on a lecture given in Oxford in May 1995) outlines the development of linear functional analysis over the years 1895-1938. It is remarked that although up to 1909 much had been achieved in dealing with various problems in the field, no general unifying theme was visible at this date.
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Multilevel Functional Clustering Analysis
Biometrics, 2012Summary In this article, we investigate clustering methods for multilevel functional data, which consist of repeated random functions observed for a large number of units (e.g., genes) at multiple subunits (e.g., bacteria types). To describe the withinâ and between variability induced by the hierarchical structure in the data, we take a multilevel ...
Serban, Nicoleta, Jiang, Huijing
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Functional Extended Redundancy Analysis
Psychometrika, 2012We propose a functional version of extended redundancy analysis that examines directional relationships among several sets of multivariate variables. As in extended redundancy analysis, the proposed method posits that a weighed composite of each set of exogenous variables influences a set of endogenous variables.
Hwang, Heungsun +4 more
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Functional Analysis and Proper Functions
The British Journal for the Philosophy of Science, 1993The etiological approach to 'proper functions' in biology can be strengthened by relating it to Robert Cummins' general treatment of function ascription. The proper functions of a biological trait are the functions it is assigned in a Cumminsstyle functional explanation of the fitness of ancestors.
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