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4,308
Geometric interpretation of signals: applications
, 2005
"... personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires pri ..."
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prior specific permission. Geometric interpretation of signals: applications by
Based on the Geometric Interpretation
"... A method that can be used to detect damage in structures is developed. This method is based on the convexity of the geometric interpretation of the eigenvalue problem for undamped positive definite systems. The damage detection scheme establishes various damage scenarios which are used as failure se ..."
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A method that can be used to detect damage in structures is developed. This method is based on the convexity of the geometric interpretation of the eigenvalue problem for undamped positive definite systems. The damage detection scheme establishes various damage scenarios which are used as failure
On the geometric interpretation of the nonnegative rank
, 2010
"... The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rankone factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult; however it has many potential applications, e.g., in data mining ..."
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Cited by 8 (0 self)
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that computing this quantity is equivalent to a problem in polyhedral combinatorics, and fully characterize its computational complexity. This in turn sheds new light on the nonnegative rank problem, and in particular allows us to provide new improved lower bounds based on its geometric interpretation. We apply
Geometric interpretations of quandle homology
, 2008
"... Geometric representations of cycles in quandle homology theory are given in terms of colored knot diagrams. Abstract knot diagrams are generalized to diagrams with exceptional points which, when colored, correspond to degenerate cycles. Bounding chains are realized, and used to obtain equivalence mo ..."
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Cited by 44 (10 self)
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Geometric representations of cycles in quandle homology theory are given in terms of colored knot diagrams. Abstract knot diagrams are generalized to diagrams with exceptional points which, when colored, correspond to degenerate cycles. Bounding chains are realized, and used to obtain equivalence
Geometric Interpretation of ¯µ(ijk)
, 2001
"... We give a geometric interpretation of Milnor’s invariants ¯µ(ijk) in terms of triple intersection points of Seifert surfaces for the three link components. This generalizes ideas from Cochran [Co] to links which are not algebraically split. Keywords: ¯µinvariants; link homotopy; Seifert surfaces. W ..."
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We give a geometric interpretation of Milnor’s invariants ¯µ(ijk) in terms of triple intersection points of Seifert surfaces for the three link components. This generalizes ideas from Cochran [Co] to links which are not algebraically split. Keywords: ¯µinvariants; link homotopy; Seifert surfaces
Geometrical interpretation of Benenti systems
 J. Geom. Phys
"... We show that the following two separately developed theories, the theory of Benenti systems in mathematical physics and the theory of projectively equivalent metrics in classical differential geometry, study essentially the same object. Combining methods and results from these two theories, one ca ..."
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Cited by 36 (15 self)
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We show that the following two separately developed theories, the theory of Benenti systems in mathematical physics and the theory of projectively equivalent metrics in classical differential geometry, study essentially the same object. Combining methods and results from these two theories, one can prove the commutative integrability of projectively equivalent pseudoRiemannian metrics and construct infinitely many new Hamiltonian systems, integrable in the classical and in the quantum sense Keywords:Integrable systems, Benenti system, projectively equivalent metrics, geodesic equivalence, quantum integrability, Nijenhuis tensor
Geometrical Interpretation of Consistent Sampling
"... We first introduce the concept of consistent sampling in infinite dimensional spaces and derive a general mathematical framework. The underlying linear reconstruction scheme coincides with the socalled oblique projection, which turns into an ordinary orthogonal projection when adapting the inner pr ..."
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product. The inner product of interest is, in general, not unique. We characterize the inner products and corresponding positive operators for which the new geometrical interpretation applies. Finally, we study explicit constructions of such positive operators by means of Riesz bases. 1 Consistent
Geometric interpretation of Schwarzschild instantons
 JOURN. GEOM. PHYS
, 2001
"... In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct selfdual L² harmonic 2forms on the space. Gibbons found a nontopological L² harmonic form in the TaubNUT metric, leading to Abelian instantons wit ..."
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Cited by 19 (14 self)
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In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct selfdual L² harmonic 2forms on the space. Gibbons found a nontopological L² harmonic form in the TaubNUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manifold and find a nontopological selfdual L² harmonic 2form on it. We show how this gives rise to Abelian instantons and identify them with SU(2)instantons of Pontryagin number 2n 2 found by Charap and Duff in 1977. Using results of Dodziuk and Hitchin we also calculate the full L² harmonic space for the
Results 1  10
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4,308