Mathematical Inequalities & Applications, 2005
Ando [1] proved that for m commuting positive definite matrices, the m-fold Hadamard product of t... more Ando [1] proved that for m commuting positive definite matrices, the m-fold Hadamard product of their geometric mean is bounded above by their Hadamard product. We obtain a natural extension to the non-commutative case.
We give an almost complete solution of a problem posed by Klaus and Li [A.-L. Klaus, C.-K. Li, Is... more We give an almost complete solution of a problem posed by Klaus and Li [A.-L. Klaus, C.-K. Li, Isometries for the vector (p, q) norm and the induced (p, q) norm, Linear and Multilinear Algebra 38 (1995) 315-332]. Klaus and Li's problem, which arose during their investigations of isometries, was to relate the Frobenius (or Hilbert-Schmidt) norm of a matrix to various operator norms of that matrix. Our methods are based on earlier work of Feng [
This paper discusses some Cauchy-Khinchin integral inequalities. Khinchin [2] obtained an inequal... more This paper discusses some Cauchy-Khinchin integral inequalities. Khinchin [2] obtained an inequality relating the row and column sums of 0-1 matrices in the course of his work on number theory. As pointed out by van Dam [6], Khinchin's inequality can be viewed as a generalization of the classical Cauchy inequality. Van Dam went on to derive analogs of Khinchin's inequality for arbitrary matrices. We carry this work forward, first by proving even more than general matrix results, and then by formulating them in a way that allows us to apply limiting arguments to create new integral inequalities for functions of two variables. These integral inequalities can be interpreted as giving information about conditional expectations. Published by Elsevier Inc.
The translation process has often been described as a sequence of three steps, source text (ST) a... more The translation process has often been described as a sequence of three steps, source text (ST) analysis, source-target transfer, and target text (TT) generation. We propose a radically different view, in which the human translation process consists of a hierarchy of interacting word and phrase translations systems which organize and integrate as dissipative structures. Activation of word (or phrase) translation systems is a non-selective subliminal process in the translator’s mind not restricted to one language. Depending on the entropy (i.e., the internal order) of the word translation systems, a human translator spends more or less time and energy during the translation process, which can be measured in the form of gaze patterns and production duration.
... Generalised roundness and negative type CJ Lennard , AM Tongey and A. Weston 1. Introduction.... more ... Generalised roundness and negative type CJ Lennard , AM Tongey and A. Weston 1. Introduction. In this paper we exhibit the equivalence of En o's non-linear notion of generalised round-ness and the classical embedding notion of negative type. This enables us to develop a ...
We establish matrix versions of refinements due to Alzer [1], Cartwright and Field [4], and Merce... more We establish matrix versions of refinements due to Alzer [1], Cartwright and Field [4], and Mercer [5] of the standard arithmetic-geometric-harmonic mean inequality for scalars.
We develop a general theory of multilinear and polynomial mappings on Banach spaces which have fa... more We develop a general theory of multilinear and polynomial mappings on Banach spaces which have factorisation properties similar to those of r-summing linear operators. We illustrate the theory by giving basic examples and deriving conditions for identifying such mappings on standard sequence spaces. In addition, we obtain norm estimates which complement previous results on lower bounds for the usual operator
Mathematical Inequalities & Applications, 2005
Ando [1] proved that for m commuting positive definite matrices, the m-fold Hadamard product of t... more Ando [1] proved that for m commuting positive definite matrices, the m-fold Hadamard product of their geometric mean is bounded above by their Hadamard product. We obtain a natural extension to the non-commutative case.
We give an almost complete solution of a problem posed by Klaus and Li [A.-L. Klaus, C.-K. Li, Is... more We give an almost complete solution of a problem posed by Klaus and Li [A.-L. Klaus, C.-K. Li, Isometries for the vector (p, q) norm and the induced (p, q) norm, Linear and Multilinear Algebra 38 (1995) 315-332]. Klaus and Li's problem, which arose during their investigations of isometries, was to relate the Frobenius (or Hilbert-Schmidt) norm of a matrix to various operator norms of that matrix. Our methods are based on earlier work of Feng [
This paper discusses some Cauchy-Khinchin integral inequalities. Khinchin [2] obtained an inequal... more This paper discusses some Cauchy-Khinchin integral inequalities. Khinchin [2] obtained an inequality relating the row and column sums of 0-1 matrices in the course of his work on number theory. As pointed out by van Dam [6], Khinchin's inequality can be viewed as a generalization of the classical Cauchy inequality. Van Dam went on to derive analogs of Khinchin's inequality for arbitrary matrices. We carry this work forward, first by proving even more than general matrix results, and then by formulating them in a way that allows us to apply limiting arguments to create new integral inequalities for functions of two variables. These integral inequalities can be interpreted as giving information about conditional expectations. Published by Elsevier Inc.
The translation process has often been described as a sequence of three steps, source text (ST) a... more The translation process has often been described as a sequence of three steps, source text (ST) analysis, source-target transfer, and target text (TT) generation. We propose a radically different view, in which the human translation process consists of a hierarchy of interacting word and phrase translations systems which organize and integrate as dissipative structures. Activation of word (or phrase) translation systems is a non-selective subliminal process in the translator’s mind not restricted to one language. Depending on the entropy (i.e., the internal order) of the word translation systems, a human translator spends more or less time and energy during the translation process, which can be measured in the form of gaze patterns and production duration.
... Generalised roundness and negative type CJ Lennard , AM Tongey and A. Weston 1. Introduction.... more ... Generalised roundness and negative type CJ Lennard , AM Tongey and A. Weston 1. Introduction. In this paper we exhibit the equivalence of En o's non-linear notion of generalised round-ness and the classical embedding notion of negative type. This enables us to develop a ...
We establish matrix versions of refinements due to Alzer [1], Cartwright and Field [4], and Merce... more We establish matrix versions of refinements due to Alzer [1], Cartwright and Field [4], and Mercer [5] of the standard arithmetic-geometric-harmonic mean inequality for scalars.
We develop a general theory of multilinear and polynomial mappings on Banach spaces which have fa... more We develop a general theory of multilinear and polynomial mappings on Banach spaces which have factorisation properties similar to those of r-summing linear operators. We illustrate the theory by giving basic examples and deriving conditions for identifying such mappings on standard sequence spaces. In addition, we obtain norm estimates which complement previous results on lower bounds for the usual operator
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Papers by Andrew Tonge