منابع مشابه
Invariant Functionals on Speh Representations
We study Sp2n(R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL2n(R). For even n we give expressions for such invariant functionals using an explicit realization of the space of smooth vectors in the Speh representations. Furthermore, we show that the functional we construct is, up to a constant, the unique functional on the Speh representation which is inva...
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In modern multivariate statistical analysis, affine invariance or equivariance for statistical procedures are properties of paramount interest and importance. A statistical procedure lacking such a property can sometimes acquire it if carried out not on the original data but rather on suitably transformed data, in some cases accompanied by a retransformation back to the original coordinate syst...
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Equivariance and invariance issues often arise in multivariate statistical analysis. Statistical procedures have to be modified sometimes to obtain an affine equivariant or invariant version. This is often done by preprocessing the data, e.g., by standardizing the multivariate data or by transforming the data to an invariant coordinate system. In this article standardization of multivariate dis...
متن کاملConservation laws for invariant functionals containing compositions
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized EulerLagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Rey...
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The use of translation invariant cost functionals for the reduction of vortices in the context of shape optimization of fluid flow domain is investigated. Analytical expressions for the shape design sensitivity involving different cost functionals are derived. Channel flow problems with a bump and an obstacle as possible control boundaries are taken as test examples. Numerical results are provi...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1956
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1956.6.231