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The geometry of nondegeneracy conditions in completely integrable systems. preprint math.DG/0403412
 Math. Ann
, 2004
"... Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems defined ..."
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Cited by 3 (1 self)
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Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems
Complementarity and Nondegeneracy in Semidefinite Programming
, 1995
"... Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict complem ..."
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Cited by 110 (9 self)
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Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict
On nondegeneracy of curves
 Algebra & Number Theory
, 2009
"... Abstract. We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We prove that every curve of genus g ≤ 4 over an algebraically closed field is nondegenerate in the above sense. More generally, let be ..."
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Cited by 8 (7 self)
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Abstract. We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We prove that every curve of genus g ≤ 4 over an algebraically closed field is nondegenerate in the above sense. More generally, let
Nondegeneracy of Polyhedra and Linear Programs
, 1995
"... This paper deals with nondegeneracy of polyhedra and linear programming (LP) problems. We allow for the possibility that the polyhedra and the feasible polyhedra of the LP problems under consideration be nonpointed. (A polyhedron is pointed if it has a vertex.) With respect to a given polyhedron, w ..."
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Cited by 1 (1 self)
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this terminology since the term dual nondegeneracy is already used to refer to a related but different type of nondegeneracy.) We show two main results about constant cost nondegeneracy of an LP problem. The first one shows that constant cost nondegeneracy of an LP problem is equivalent to the condition
ADDENDA AND ERRATA FOR ON NONDEGENERACY OF CURVES
"... This note gives some addenda and errata for the article On nondegeneracy of curves [3]. ..."
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This note gives some addenda and errata for the article On nondegeneracy of curves [3].
Nondegeneracy Criteria for 3D Grid Formulas for a Cell Volume
"... Nondegeneracy criteria for threedimensional grid cells are found for hexahedral cells which are given by eight corner points and generated by the trilinear map from a unit cube to a region defined by these points. The criteria include both nondegeneracy conditions and a special numerical algorithm ..."
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Nondegeneracy criteria for threedimensional grid cells are found for hexahedral cells which are given by eight corner points and generated by the trilinear map from a unit cube to a region defined by these points. The criteria include both nondegeneracy conditions and a special numerical algorithm
Nondegeneracy of the discriminant
, 2014
"... To Professor Arkadiusz P loski on his 65th birthday Let (`, f): (C2, 0) − → (C2, 0) be the germ of a holomorphic mapping such that ` = 0 is a smooth curve and f = 0 has an isolated singularity at 0 ∈ C2. We assume that ` = 0 is not a branch of f = 0. The direct image of the critical locus of this ..."
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To Professor Arkadiusz P loski on his 65th birthday Let (`, f): (C2, 0) − → (C2, 0) be the germ of a holomorphic mapping such that ` = 0 is a smooth curve and f = 0 has an isolated singularity at 0 ∈ C2. We assume that ` = 0 is not a branch of f = 0. The direct image of the critical locus of this mapping is called the discriminant curve. In this paper we study the pairs (`, f) for which the discriminant curve is nondegenerate in the Kouchnirenko sense. 1
PBW Bases, Non–Degeneracy Conditions and Applications
 Proceedings of the ICRA X conference. Volume 45., AMS. Fields Institute Communications
, 2005
"... Abstract. We establish an explicit criteria (the vanishing of non–degeneracy conditions) for certain noncommutative algebras to have Poincaré–Birkhoff– Witt basis. We study theoretical properties of such G–algebras, concluding they are in some sense ”close to commutative”. We use the non–degenerac ..."
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Cited by 6 (3 self)
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Abstract. We establish an explicit criteria (the vanishing of non–degeneracy conditions) for certain noncommutative algebras to have Poincaré–Birkhoff– Witt basis. We study theoretical properties of such G–algebras, concluding they are in some sense ”close to commutative”. We use the non–degeneracy
Results 1  10
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12,114