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Abstract: In this paper, we give some characterizations of the integral and Carleson type measure both associated with higher radial derivative for holomorphic functions of and spaces in the unit ball of . As applications, some sharp forms of the relations between Dirichlet type spaces and spaces are shown by means of higher radial derivative, Carleson type measure and constructive methods for the cases of determinism and randomization, respectively. [Copyright &y& Elsevier]

Abstract: In this paper, we study a boundary feedback system of a class of nonuniform undamped Timoshenko beam with both ends free. We give some sufficient conditions and some necessary conditions for the system to have exponential stability. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method. [Copyright &y& Elsevier]