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Programming in MartinLöf Type Theory: Unification  A nontrivial Example
 DEPARTMENT OF COMPUTER SCIENCE, CHALMERS UNIVERSITY OF TECHNOLOGY
, 1999
"... MartinLöf's type theory is a constructive type theory originally conceived as a formal language in which to carry out constructive mathematics. However, it can also be viewed as a programming language where specifications are represented as types and programs as objects of the types. In this w ..."
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Cited by 5 (2 self)
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. In this work, the use of type theory as a programming language is investigated. As an example, a formalisation of a unification algorithm for firstorder terms is considered. Unification can be seen as the process of finding a substitution that makes all the pairs of terms in an input list equal, if such a
Programming in MartinLof Type Theory Unification A nontrivial Example
 Department of Computer Science, Chalmers University of Technology
, 1999
"... MartinLof's type theory is a constructive type theory originally conceived as a formal language in which to carry out constructive mathematics. However, it can also be viewed as a programming language where specifications are represented as types and programs as objects of the types. In this w ..."
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. In this work, the use of type theory as a programming language is investigated. As an example, a formalisation of a unification algorithm for firstorder terms is considered. Unification can be seen as the process of finding a substitution that makes all the pairs of terms in an input list equal, if such a
pHarmonic morphisms: the 1 < p < 2 case and some nontrivial examples
"... Introduction Harmonic maps, defined as the extremums of the energy functional, find a natural generalisation in pharmonic maps, the critical points of the penergy functional. Though several key properties remain valid, crucial dissimilarities in their regularity make the analysis of pharmonic ma ..."
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Introduction Harmonic maps, defined as the extremums of the energy functional, find a natural generalisation in pharmonic maps, the critical points of the penergy functional. Though several key properties remain valid, crucial dissimilarities in their regularity make the analysis of pharmonic maps a delicate matter. A particular subclass of harmonic maps, the harmonic morphisms, has been found to enjoy notable geometrical attributes. Harmonic morphisms were defined by potential theorists, as preserving local harmonic functions and characterised as horizontally weakly conformal harmonic maps by B. Fuglede [F78] and T. Ishihara [I] (see [F99] for an overview of this theory). The temptation of defining pharmonic morphisms as preserving local pharmonic functions and recovering a FugledeIshihara Characterisation is the driving force
A NONTRIVIAL EXAMPLE OF A FREEBYFREE GROUP WITH THE HAAGERUP PROPERTY
"... Abstract. The aim of this note is to prove that the group of FormanekProcesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a nonlinear semidirect product between two non abelian free groups which satisfies the Haagerup property. ..."
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Abstract. The aim of this note is to prove that the group of FormanekProcesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a nonlinear semidirect product between two non abelian free groups which satisfies the Haagerup property.
A NONTRIVIAL EXAMPLE OF A FREEBYFREE GROUP WITH THE HAAGERUP PROPERTY
"... Abstract. The aim of this note is to prove that the group of FormanekProcesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a nonlinear semidirect product between two non abelian free groups which satisfies the Haagerup property. ..."
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Abstract. The aim of this note is to prove that the group of FormanekProcesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a nonlinear semidirect product between two non abelian free groups which satisfies the Haagerup property.
1 NON TRIVIAL EXAMPLES OF COUPLED EQUATIONS FOR KÄHLER METRICS AND YANGMILLS CONNECTIONS
"... ar ..."
of a trivial strongly analytic multifunction
, 2007
"... nontrivial example of a trivial strongly ..."
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3393 (12 self)
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The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when
Free construction of CAT (1)spaces
 Arch. Math. (Basel
"... Abstract. We construct several nontrivial examples of CAT(1) spaces by using the idea of free construction. 1. ..."
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Cited by 3 (0 self)
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Abstract. We construct several nontrivial examples of CAT(1) spaces by using the idea of free construction. 1.
COEFFICIENTS AND NONTRIVIALITY OF THE JONES POLYNOMIAL
, 2006
"... We show that several classes of links, including semiadequate links and Whitehead doubles of semiadequate knots, have nontrivial Jones polynomial. Then we prove that there are infinitely many positive knots with no positive minimal crossing diagrams, and infinitely many achiral knots of odd crossi ..."
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Cited by 9 (1 self)
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We show that several classes of links, including semiadequate links and Whitehead doubles of semiadequate knots, have nontrivial Jones polynomial. Then we prove that there are infinitely many positive knots with no positive minimal crossing diagrams, and infinitely many achiral knots of odd
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