Let ϕ be an analytic self-map of the unit disk D, H (D) the space of analytic functions on D and g ∈ H (D). The boundedness and compactness of the operator DC ϕ : H ∞ → Z are investigated in this paper.

The incorporation of colloidal CdTe quantum dots into an inorganic matrix, BaSO 4 , through a handy and rapid co-precipitation method is demonstrated for the first time. Owing to the protection of the BaSO 4 matrix, the resulting composites show stronger luminescence, longer fluorescent lifetime, and higher photo-and thermal stability as well as being more anti-acid compared to the parental CdTe QDs.Moreover, the composites hold several advantages for industrial applications. White light-emitting diodes (WLEDs) utilizing the composites as a red color conversion layer are fabricated, and produce bright white light with high color-rendering properties including a CIE coordinate of (0.34, 0.33), an R a of 88, and a T c of 5112 K at 20 mA, suggesting their great potential application in a solid-state lighting system with high color-rendering properties.

Let H(B) denote the space of all holomorphic functions on the unit ball B of C n , ψ ∈ H(B) and ϕ be a holomorphic self-map of B. Let C ϕ , M ψ and R denote the composition, multiplication and radial derivative operators, respectively. In this paper, we characterize the boundedness and compactness of linear operators induced by products of these operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball.

In this Letter, we show an ultralarge capacity for three-dimensional optical data storage inside transparent fluorescent tape using the two-photon absorption photo-bleaching method. We can obtain transparent fluorescent tape by means of the simple dip method. We successfully demonstrate recording and reading of six layers of binary data bits with lateral separation of 2 µm and longitudinal layer separation of 3 µm. Thus, this result leads to a storage density of approximately 80 G b i t s / c m 3 . Therefore, we can realize authentic ultrahigh capacity optical data storage using long transparent fluorescent tape in the future, like magnetic tape, and fundamentally solve the data explosion disaster.