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Skew -Derivations on Semiprime Rings
For a ring with an automorphism , an -additive mapping
is called a skew
-derivation with respect to if it is always a -derivation
of for each argument. Namely, it is always a -derivation of for
the argument being left once arguments are fixed by elements in
. In this short note, starting from Bre\v{s}ar Theorems, we prove that a
skew -derivation () on a semiprime ring must map into the
center of .Comment: 8 page
Phase Retrieval for Sparse Signals
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 minimization. In
particular, we present the null space property which, to our knowledge, is the
first sufficient and necessary condition for the success of
minimization for -sparse phase retrievable.Comment: 14 page
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