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A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical ba ...
We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...
We study differential equations that lead to extremal points in symplectic pseudospectra. In a two-level approach, where on the inner level we compute extremizers of the symplectic epsilon-pseudospectrum for a given epsilon and on the outer level we optimi ...
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Mobius group of the projective line. Since the general proof is very simple but not explicit, we also provi ...
Decades of technological developments have populated the field of neuroprosthetics with myriad replacement strategies, neuromodulation therapies, and rehabilitation procedures to improve the quality of life for individuals with neuromotor disorders. Despit ...
American Association for the Advancement of Science2013
Let Gamma be an irreducible lattice in a product of n infinite irreducible complete Kac–Moody groups of simply laced type over finite fields. We show that if n>2, then each Kac–Moody groups is in fact a simple algebraic group over a local field and Gamma i ...
Fix an algebraically closed field K having characteristic p≥0 and let Y be a simple algebraic group of classical type over K. Also let X be maximal among closed connected subgroups of Y and consider a non-trivial p-restricted irreducible ...
A natural extension of the free rigid body dynamics to the unitary group U (n) is considered. The dynamics is described by the Euler equation on the Lie algebra u(n), which has a bi-Hamiltonian structure, and it can be reduced onto the adjoint orbits, as i ...
We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...
Let G be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism F. In this article we extend an observation of Lusztig (which gives a numerical relationship between an ordinary character of GF an ...
