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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: This paper studies the characteristics and structure of the weak surface of the production possibility set. We apply techniques and methods of transferring a polyhedral cone from its intersection form to its sum form, identify an intersection representation of the production possibility set. We give the structure theorem of weak surface of the production possibility set, which includes three complementary slackness conditions. We define the input weak efficiency and output weak efficiency for different DEA models according to the representation of the intersection form. It investigates the characteristics of the weak surfaces, and proves the structure theorems of input weak DEA efficiency and output weak DEA efficiency. The structure theorems establish weighted combination of inputs and outputs that are weak DEA efficient. Numerical examples are provided for illustration. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to show that various classes of operators having a common collection of root spaces whose closed linear span equals the entire space have dense sets of common cyclic vectors. [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]

Abstract: This paper deals with a parabolic system, cross-coupled via a nonlinear source and a nonlinear boundary flux. We get a necessary and sufficient condition for the existence of non-simultaneous blow-up. In particular, four different simultaneous blow-up rates are obtained in different regions of parameters, described by an introduced characteristic algebraic system. It is observed that different initial data may result in different simultaneous blow-up rates even in the same region of parameters. [Copyright &y& Elsevier]