239,522 research outputs found

    Skew NN-Derivations on Semiprime Rings

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    For a ring RR with an automorphism Οƒ\sigma, an nn-additive mapping Ξ”:RΓ—RΓ—...Γ—Rβ†’R\Delta:R\times R\times... \times R \rightarrow R is called a skew nn-derivation with respect to Οƒ\sigma if it is always a Οƒ\sigma-derivation of RR for each argument. Namely, it is always a Οƒ\sigma-derivation of RR for the argument being left once nβˆ’1n-1 arguments are fixed by nβˆ’1n-1 elements in RR. In this short note, starting from Bre\v{s}ar Theorems, we prove that a skew nn-derivation (nβ‰₯3n\geq 3) on a semiprime ring RR must map into the center of RR.Comment: 8 page

    Phase Retrieval for Sparse Signals

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    The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse signals without the phase information. We completely settle the minimality question for the real case and give a lower bound for the complex case. We then study the recovery performance of the β„“1\ell_1 minimization. In particular, we present the null space property which, to our knowledge, is the first sufficient and necessary condition for the success of β„“1\ell_1 minimization for kk-sparse phase retrievable.Comment: 14 page
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