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Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces. [PDF]
J Evol EquGórny W.
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Basic Analysis III, 2020
In this handout we assume all vector spaces are over the field k.
James K. Peterson
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In this handout we assume all vector spaces are over the field k.
James K. Peterson
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IEEE Transactions on Evolutionary Computation, 2021
This article suggests a multimodal multiobjective evolutionary algorithm with dual clustering in decision and objective spaces. One clustering is run in decision space to gather nearby solutions, which will classify solutions into multiple local clusters.
Qiuzhen Lin +5 more
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This article suggests a multimodal multiobjective evolutionary algorithm with dual clustering in decision and objective spaces. One clustering is run in decision space to gather nearby solutions, which will classify solutions into multiple local clusters.
Qiuzhen Lin +5 more
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Bulletin of the Australian Mathematical Society, 2019
We show that if $(X,\Vert \cdot \Vert )$ is a Banach space that admits an equivalent locally uniformly rotund norm and the set of all norm-attaining functionals is residual then the dual norm $\Vert \cdot \Vert ^{\ast }$ on $X^{\ast }$ is Fréchet at
Moors, Warren B., Tan, Neşet Özkan
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We show that if $(X,\Vert \cdot \Vert )$ is a Banach space that admits an equivalent locally uniformly rotund norm and the set of all norm-attaining functionals is residual then the dual norm $\Vert \cdot \Vert ^{\ast }$ on $X^{\ast }$ is Fréchet at
Moors, Warren B., Tan, Neşet Özkan
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1995
Linear functionals and the dual space of a vector space are defined and characterized. Every vector space is shown to be canonically embeddable in its second dual. Maximal subspaces are characterized as kernels of nontrivial linear functionals. The trace of a square matrix is studied in detail. Over a field of characteristic 0, a square matrix is shown
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Linear functionals and the dual space of a vector space are defined and characterized. Every vector space is shown to be canonically embeddable in its second dual. Maximal subspaces are characterized as kernels of nontrivial linear functionals. The trace of a square matrix is studied in detail. Over a field of characteristic 0, a square matrix is shown
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CHI '11 Extended Abstracts on Human Factors in Computing Systems, 2011
Dual-Space Drawing is an interface that enables children to express their drawing ideas in both the digital and real worlds. It supports creative and reflective drawing experiences using two layers: a transparent layer and a screen layer. The interface takes a user's drawing movements on the transparent display unobtrusively and then projects the ...
Jee Yeon Hwang +2 more
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Dual-Space Drawing is an interface that enables children to express their drawing ideas in both the digital and real worlds. It supports creative and reflective drawing experiences using two layers: a transparent layer and a screen layer. The interface takes a user's drawing movements on the transparent display unobtrusively and then projects the ...
Jee Yeon Hwang +2 more
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Dual spaces for variable martingale Lorentz–Hardy spaces
Banach Journal of Mathematical Analysis, 2021Y. Jiao, F. Weisz, Lian Wu, Dejian Zhou
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