286,042 research outputs found
Sharp interface limit for a phase field model in structural optimization
We formulate a general shape and topology optimization problem in structural
optimization by using a phase field approach. This problem is considered in
view of well-posedness and we derive optimality conditions. We relate the
diffuse interface problem to a perimeter penalized sharp interface shape
optimization problem in the sense of -convergence of the reduced
objective functional. Additionally, convergence of the equations of the first
variation can be shown. The limit equations can also be derived directly from
the problem in the sharp interface setting. Numerical computations demonstrate
that the approach can be applied for complex structural optimization problems
Bianchi's classification of 3-dimensional Lie algebras revisited
We present Bianchi's proof on the classification of real (and complex)
-dimensional Lie algebras in a coordinate free version from a strictly
representation theoretic point of view. Nearby we also compute the automorphism
groups and from this the orbit dimensions of the corresponding orbits in the
algebraic variety describing all Lie brackets
on a fixed vector space of dimension . Moreover we clarify which orbits
lie in the closure of a given orbit and therefore the topology on the orbit
space with
-theory of compact Lie groups with group anti-involutions
Let be a compact, connected, and simply-connected Lie group, equipped
with an anti-involution which is the composition of a Lie group
involutive automorphism and the group inversion. We view
as a Real -space via the conjugation action. In this note, we
exploit the notion of Real equivariant formality discussed in \cite{Fo} to
compute the ring structure of the equivariant -theory of . In
particular, we show that when does not have Real representations of complex
type, the equivariant -theory is the ring of Grothendieck differentials of
the coefficient ring of equivariant -theory over the coefficient ring of
ordinary -theory, thereby generalizing a result of Brylinski-Zhang's
(\cite{BZ}) for the complex -theory case.Comment: 11 pages. Accepted by Topology and its Application
Unsupervised Learning of Complex Articulated Kinematic Structures combining Motion and Skeleton Information
In this paper we present a novel framework for unsupervised kinematic structure learning of complex articulated objects from a single-view image sequence. In contrast to prior motion information based methods, which estimate relatively simple articulations, our method can generate arbitrarily complex kinematic structures with skeletal topology by a successive iterative merge process. The iterative merge process is guided by a skeleton distance function which is generated from a novel object boundary generation method from sparse points. Our main contributions can be summarised as follows: (i) Unsupervised complex articulated kinematic structure learning by combining motion and skeleton information. (ii) Iterative fine-to-coarse merging strategy for adaptive motion segmentation and structure smoothing. (iii) Skeleton estimation from sparse feature points. (iv) A new highly articulated object dataset containing multi-stage complexity with ground truth. Our experiments show that the proposed method out-performs state-of-the-art methods both quantitatively and qualitatively
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