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Results 1 - 10
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463
THE PRINCIPAL AXIS THEOREM FOR HOLOMORPHIC FUNCTIONS
"... Abstract. An algebraic approach to Rellich’s theorem is given which states that any analytic family of matrices which is normal on the real axis can be diagonalized by an analytic family of matrices which is unitary on the real axis. We show that this result is a special version of a purely algebrai ..."
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Cited by 1 (0 self)
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Abstract. An algebraic approach to Rellich’s theorem is given which states that any analytic family of matrices which is normal on the real axis can be diagonalized by an analytic family of matrices which is unitary on the real axis. We show that this result is a special version of a purely
OBB-Tree: A hierarchical structure for rapid interference detection
- PROC. ACM SIGGRAPH, 171–180
, 1996
"... We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal and curved models. It pre-computes a hierarchical representation of models using tight-fitting oriented bo ..."
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Cited by 845 (53 self)
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bounding box trees. At runtime, the algorithm traverses the tree and tests for overlaps between oriented bounding boxes based on a new separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures
Helly-type theorems for hollow axis-aligned boxes
- PROC. AMER. MATH. SOC
, 1999
"... A hollow axis-aligned box is the boundary of the cartesian product of d compact intervals in R d. We show that for d ≥ 3, if any 2 d of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any 5 of a collection of hollow ..."
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Cited by 2 (2 self)
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A hollow axis-aligned box is the boundary of the cartesian product of d compact intervals in R d. We show that for d ≥ 3, if any 2 d of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any 5 of a collection
Jet shapes with the broadening axis
, 2014
"... Abstract: Broadening is a classic jet observable that probes the transverse momentum structure of jets. Traditionally, broadening has been measured with respect to the thrust axis, which is aligned along the (hemisphere) jet momentum to minimize the vector sum of transverse momentum within a jet. In ..."
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the jet angularities become recoil-free when measured using the broadening axis. We derive a simple factorization theorem for broadening-axis observables which smoothly interpolates between the thrust-like and broadening-like regimes. We argue that the same factorization theorem holds for two-point energy
The Geometrization Theorem
"... In this paper, we discuss the Geometrization Theorem, formerly Thurston's Geometrization Conjecture, which is essentially the statement that one can cut up a 3-manifold into pieces such that each piece is geometrically "like" one of eight model geometries. The proof of this by Perelm ..."
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In this paper, we discuss the Geometrization Theorem, formerly Thurston's Geometrization Conjecture, which is essentially the statement that one can cut up a 3-manifold into pieces such that each piece is geometrically "like" one of eight model geometries. The proof
Liouville theorems for the Navier-Stokes equations and applications
"... We study bounded ancient solutions of the Navier-Stokes equations. These are solutions with bounded velocity defined in R n × (−∞,0). In two space dimensions we prove that such solutions are either constant or of the form u(x,t) = b(t), depending on the exact definition of admissible solutions. The ..."
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Cited by 42 (3 self)
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. The general three dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axi-symmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a
Cut locus and medial axis in global shape interrogation and representation
- MIT Design Laboratory Memorandum 92-2 and MIT Sea Grant Report
, 1992
"... The cut locus CA of a closed set A in the Euclidean space E is defined as the closure of the set containing all points p which have at least two shortest paths to A. We present a theorem stating that the complement of the cut locus i.e. E\(CA∪A) is the maximal open set in (E\A) where the distance fu ..."
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Cited by 47 (3 self)
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function with respect to the set A is continuously differentiable. This theorem includes also the result that this distance function has a locally Lipschitz continuous gradient on (E\A). The medial axis of a solid D in E is defined as the union of all centers of all maximal discs which fit in this domain
Fast 3D triangle-box overlap testing
- J. Graph. Tools
, 2002
"... Abstract A fast routine for testing whether a triangle and a box are overlapping in three dimensions is presented. The test is derived using the separating axis theorem, whereafter the test is simplified and the code is optimized for speed. We show that this approach is 2.3 vs. 3.8 (PC vs. Sun) tim ..."
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Cited by 42 (0 self)
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Abstract A fast routine for testing whether a triangle and a box are overlapping in three dimensions is presented. The test is derived using the separating axis theorem, whereafter the test is simplified and the code is optimized for speed. We show that this approach is 2.3 vs. 3.8 (PC vs. Sun
Geometry of Călugăreanu’s theorem
, 2005
"... A central result in the space geometry of closed twisted ribbons is Călugăreanu’s theorem (also known as White’s formula, or the Călugăreanu–White–Fuller theorem). This enables the integer linking number of the two edges of the ribbon to be written as the sum of the ribbon twist (the rate of rotatio ..."
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Cited by 7 (0 self)
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A central result in the space geometry of closed twisted ribbons is Călugăreanu’s theorem (also known as White’s formula, or the Călugăreanu–White–Fuller theorem). This enables the integer linking number of the two edges of the ribbon to be written as the sum of the ribbon twist (the rate
Results 1 - 10
of
463
