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MORSE THEORY FOR RIEMANNIAN GEODESICS WITHOUT NONDEGENERACY ASSUMPTIONS
"... Let f ∈ C2 (M, R) be a functional defined on a Hilbert manifold M. It is well known that if f is a Morse functional (i.e. every critical point of f is nondegenerate) and f satisfies the so called Palais–Smale condition, the Morse relations hold. More precisely, let x ∈ M be a critical point of f, an ..."
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Let f ∈ C2 (M, R) be a functional defined on a Hilbert manifold M. It is well known that if f is a Morse functional (i.e. every critical point of f is nondegenerate) and f satisfies the so called Palais–Smale condition, the Morse relations hold. More precisely, let x ∈ M be a critical point of f, and m(x, f)
An Affine Scaling Method with an Infeasible Starting Point: Convergence Analysis under Nondegeneracy Assumption
, 1993
"... In this paper, we propose an infeasibleinteriorpoint algorithm for linear programming based on the affine scaling algorithm by Dikin. The search direction of the algorithm is composed of two directions, one for satisfying feasibility and the other for aiming at optimality. Both directions are affi ..."
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Cited by 1 (0 self)
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are affine scaling directions of certain linear programming problems. Global convergence of the algorithm is proved under a reasonable nondegeneracy assumption. A summary of analogous global convergence results for general cases obtained in [17] by means of the local potential function is also given. Key
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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complementarity is assumed. Primal and dual nondegeneracy assumptions do not imply strict complementarity, as they do in LP. The primal and dual nondegeneracy assumptions imply a range of possible ranks for primal and dual solutions X and Z. This is in contrast with LP where nondegeneracy assumptions exactly
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 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
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
On Removing Nondegeneracy Assumptions in Computational Geometry (Extended Abstract)
, 1997
"... ) Francisco G'omez 1 , Suneeta Ramaswami 2 and Godfried Toussaint 2 1 Dept. of Applied Mathematics, Universidad Politecnica de Madrid, Madrid, Spain 2 School of Computer Science, McGill University, Montr'eal, Qu'ebec, Canada Abstract Existing methods for removing degeneracies ..."
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Cited by 9 (7 self)
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address an alternative approach that has received little attention in the computational geometry literature. Often a typical computational geometry paper will make a nondegeneracy assumption that can in fact be removed (without perturbing the input) by a global rigid transformation of the input
SingleParticle Nondegeneracy and SU(3)
, 1994
"... It is shown that the SU(3) symmetry of the fermion dynamical symmetry model is essentially preserved even for highly nondegenerate spherical singleparticle energies. The breaking of SU(3) symmetry by singleparticle energy terms for either normal deformation or superdeformation occurs only through ..."
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It is shown that the SU(3) symmetry of the fermion dynamical symmetry model is essentially preserved even for highly nondegenerate spherical singleparticle energies. The breaking of SU(3) symmetry by singleparticle energy terms for either normal deformation or superdeformation occurs only through an indirect Pauli effect and is significant only when the spherical singleparticle splitting within shells is artificially large relative to that observed experimentally. 1 The shell model is commonly accepted as the microscopic basis for nuclear structure, but its practical implementation in medium and heavy nuclei requires a severe truncation of the model space. In the late 1980’s, motivated by the phenomenological successes of the Interacting Boson Model [1] and building on the schematic fermion model of Ginocchio [2], we proposed a symmetrydictated truncation scheme for the shell model termed the Fermion Dynamical Symmetry Model (FDSM) [3,4]. The symmetry limits of the model and perturbations around these limits have been explored extensively, and found to be consistent with a broad range of nuclear structure observations [5]. It is now of interest to examine in detail the excursions from the symmetry limits of the theory,
Results 1  10
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9,959