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 ...
Mathematical Proceedings of the Cambridge Philosophical Society, Oct 31, 1998
In this paper we give a different interpretation of Bombieri's norm. This new point of view allow... more In this paper we give a different interpretation of Bombieri's norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence S n (P) = sup Qn [P Q n ] 2 , where P is a fixed m−homogeneous polynomial and Q n runs over the unit ball of the Hilbert space of n−homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on C N and we obtain sharp inequalities whenever the number of factors is no greater than N. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set {z k } n k=1 of unit vectors in a complex Hilbert space for which sup z =1 | z, z 1 • • • z, z n | is minimum must be an orthonormal system.
Mathematical Proceedings of the Cambridge Philosophical Society, 1998
In this paper we give a different interpretation of Bombieri's norm. This new point of view allow... more In this paper we give a different interpretation of Bombieri's norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence S n (P) = sup Qn [P Q n ] 2 , where P is a fixed m−homogeneous polynomial and Q n runs over the unit ball of the Hilbert space of n−homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on C N and we obtain sharp inequalities whenever the number of factors is no greater than N. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set {z k } n k=1 of unit vectors in a complex Hilbert space for which sup z =1 | z, z 1 • • • z, z n | is minimum must be an orthonormal system.
Strong l p sequences, Weak l p sequences, Characterization of p-summing operators CONSTRUCTIONS O... more Strong l p sequences, Weak l p sequences, Characterization of p-summing operators CONSTRUCTIONS OF P-SUMMING OPERATORS Finite rank operators, The Banach ideal of p-summing operators, Injectivity, Inclusion Theorem BASIC EXAMPLES ,40 Multiplication operators, Formal inclusion operators, Diagonal operators, Embeddings of function spaces, Kernel operators DOMINATION AND FACTORIZATION \ Pietsch Domination Theorem, Pietsch Factorization Theorem, Operators from and to C(K')-spaces, 2-summing operators SOME CONSEQUENCES Weak compactness and complete continuity of p-summing operators, Weak Dvoretzky-Rogers Theorem, p-summing character of biadjoints and adjoints COMPOSITION \ NOTES AND REMARKS 3. Summing Operators on £ P-Spaces £p-SPACES Operators from £i-spaces to £2-spaces are 1-summing, Approximation in L p (ii) and C(K), Lp(ji) and C(K) as basic examples of £ p-spaces OPERATORS ON £OO-SPACES Operators from Coo-spaces to £ p-spaces (l<p<2) are 2-summing SOME APPLICATIONS , Quotients of C{K) which are subspaces of £1, Coincidence of 2-summing and 1-summing operators on subspaces of £ p (l<p<2), uniqueness of unconditional basis in ti, vi Contents Li[O,l] has no unconditional basis, Coincidence of g-summing and 2-summing operators on subspaces of C p for l<p<2<q<oo, Extrapolation Theorem NOTES AND REMARKS 73 4. Operators on Hilbert Spaces and Summing Operators 76
We give a unified treatment of procedures for complexifying real Banach spaces. These include sev... more We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.
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 investigate the equivalence constants for the l p -coefficient norms and l q -operator norms (... more We investigate the equivalence constants for the l p -coefficient norms and l q -operator norms (1 p, q ∞) of complex m × n matrices, and provide estimates which are either best possible or close to best possible.
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
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&#x27;s non-linear notion of generalised round-ness and the classical embedding notion of negative type. This enables us to develop a ...
Mathematical Proceedings of the Cambridge Philosophical Society, Oct 31, 1998
In this paper we give a different interpretation of Bombieri's norm. This new point of view allow... more In this paper we give a different interpretation of Bombieri's norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence S n (P) = sup Qn [P Q n ] 2 , where P is a fixed m−homogeneous polynomial and Q n runs over the unit ball of the Hilbert space of n−homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on C N and we obtain sharp inequalities whenever the number of factors is no greater than N. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set {z k } n k=1 of unit vectors in a complex Hilbert space for which sup z =1 | z, z 1 • • • z, z n | is minimum must be an orthonormal system.
Mathematical Proceedings of the Cambridge Philosophical Society, 1998
In this paper we give a different interpretation of Bombieri's norm. This new point of view allow... more In this paper we give a different interpretation of Bombieri's norm. This new point of view allows us to work on a problem posed by Beauzamy about the behavior of the sequence S n (P) = sup Qn [P Q n ] 2 , where P is a fixed m−homogeneous polynomial and Q n runs over the unit ball of the Hilbert space of n−homogeneous polynomials. We also study the factor problem for homogeneous polynomials defined on C N and we obtain sharp inequalities whenever the number of factors is no greater than N. In particular, we prove that for the product of homogeneous polynomials on infinite dimensional complex Hilbert spaces our inequality is sharp. Finally, we use these ideas to prove that any set {z k } n k=1 of unit vectors in a complex Hilbert space for which sup z =1 | z, z 1 • • • z, z n | is minimum must be an orthonormal system.
Strong l p sequences, Weak l p sequences, Characterization of p-summing operators CONSTRUCTIONS O... more Strong l p sequences, Weak l p sequences, Characterization of p-summing operators CONSTRUCTIONS OF P-SUMMING OPERATORS Finite rank operators, The Banach ideal of p-summing operators, Injectivity, Inclusion Theorem BASIC EXAMPLES ,40 Multiplication operators, Formal inclusion operators, Diagonal operators, Embeddings of function spaces, Kernel operators DOMINATION AND FACTORIZATION \ Pietsch Domination Theorem, Pietsch Factorization Theorem, Operators from and to C(K')-spaces, 2-summing operators SOME CONSEQUENCES Weak compactness and complete continuity of p-summing operators, Weak Dvoretzky-Rogers Theorem, p-summing character of biadjoints and adjoints COMPOSITION \ NOTES AND REMARKS 3. Summing Operators on £ P-Spaces £p-SPACES Operators from £i-spaces to £2-spaces are 1-summing, Approximation in L p (ii) and C(K), Lp(ji) and C(K) as basic examples of £ p-spaces OPERATORS ON £OO-SPACES Operators from Coo-spaces to £ p-spaces (l<p<2) are 2-summing SOME APPLICATIONS , Quotients of C{K) which are subspaces of £1, Coincidence of 2-summing and 1-summing operators on subspaces of £ p (l<p<2), uniqueness of unconditional basis in ti, vi Contents Li[O,l] has no unconditional basis, Coincidence of g-summing and 2-summing operators on subspaces of C p for l<p<2<q<oo, Extrapolation Theorem NOTES AND REMARKS 73 4. Operators on Hilbert Spaces and Summing Operators 76
We give a unified treatment of procedures for complexifying real Banach spaces. These include sev... more We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.
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 investigate the equivalence constants for the l p -coefficient norms and l q -operator norms (... more We investigate the equivalence constants for the l p -coefficient norms and l q -operator norms (1 p, q ∞) of complex m × n matrices, and provide estimates which are either best possible or close to best possible.
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