Composition of entire functions with finite iterated order

In this paper, we investigate the growth of two composite entire functions of finite iterated order and a series of comparative growths of logp+qT(r,f(g)) (p,q∈N) with logpT(r,f) and logqT(r,g). At the end of this paper, we apply some growth results into the factorization of the solutions of linear differential equation. We achieve some results which are the improvements and extensions of the previous results.     

Norms of composition operators with rational symbol

We compute the norms of composition operators with rational symbols that satisfy certain properties, extending Christopher Hammond's methods on operators with linear fractional symbols. This leads to a host of new examples of composition operators whose norms are calculable.     

BOUNDEDNESS OF COMPOSITION OPERATORS ON Dτ SPACES FOR τ>1

In this note, some conditions of composition operators on Dτspaces to be bounded are given by means of Carleson measures and pointwisemultipliers, for some ranges of τ. The authors prove that (i) Let 1<τ n+2 and 2k<τ 2k+1 (or 2k-1<τ 2k) for somepositive integer k. Suppose φ=(φ1,...,φn) be aunivalent mapping from B into itself, denote dμj(l)(z)=R(l)φj(z)2(k-l+2)(1-|z|2)2k-τ+1 dν(z) for l=1,2,...,k+1. If μj(l)φ-1 are (τ-2k+2l-4)-Carleson measures for all l, then the composition operator Cφon Dτis bounded; (ii) Let 1<τ n+2, φ=(φ1,...,φn)be univalent and the Fr echet derivativeof φ-1 be bounded onφ(B). If Rφj∈M(Dτ-2) forall j, then the composition operator Cφ on Dτis bounded; (iii) Let τ>n+2 and φ as in (ii).If φj∈Dτ for all j, then the compositionoperator Cφ on Dτ is bounded.     

Bi0·5K0·5TiO3-based lead-free relaxor ferroelectric with high energy storage performances via the grain size and bandgap engineering

Dielectric capacitors with high energy storage performance show a huge competitive advantage for use in vehicles and power electronics. Here, the (1-x) (0.75Bi_0·5K_0·5TiO₃?0.25BiFeO₃) – xSr_0.7Bi_0·2TiO₃ (BKT-BF-xSBT) materials were designed based on the dual optimization strategy of grain size and bandgap. The optimal performance was obtained in the BKT-BF-0.4SBT sample, achieving high energy storage density W_rec of 5.21 J/cm³ and high energy storage efficiency η of 90.87% at 360 kV/cm. The addition of SBT optimized the microstructure and relaxation behavior of BKT-BF ceramic, giving rise to the formation of polar nanoregions (PNRs), small grain size (G), compact grain boundaries, and wide bandgap (E_g) synchronously. Encouragingly, prominent stabilities against temperature, frequency, and cycle numbers, and favorable charge/discharge performance (power density P_D ≈ 64.5 MW/cm³, τ_0.9 ≈ 90 ns) are also accomplished in designed BKT-based ceramics. These findings indicate that the BKT-BF-xSBT ceramic system has excellent potential in the dielectric energy storage field and also provides a viable prospect for engineering design of high-efficiency lead-free dielectrics via bandgap and grain size.     

Generalized Composition Operators Between Mixed-Norm and Some Weighted Spaces

The boundedness and compactness of the generalized composition operator from mixed-norm spaces to the Bloch-type space, the little Bloch-type space, the Zygmund space, and the little Zygmund space are investigated in this paper.     

Generalized Weighted Composition Operators on Weighted Bergman Spaces

The boundedness and compactness of the generalized weighted composition operator on weighted Bergman spaces are discussed.     

Growth and microstructural features of laser ablated LiCoO2 thin films

Thin films of LiCoO₂ were prepared by pulsed laser deposition technique and the properties were studied in relation to the deposition parameters. The films deposited from a sintered composite target (LiCoO₂+Li₂O) in an oxygen partial pressure of 100 mTorr and at a substrate temperature of 300 °C exhibited preferred c-axis (0 0 3) orientation perpendicular to the substrate surface. The AFM data demonstrated that the films are composed of uniform distribution of fine grains with an average grain size of 80 nm. The grain size increased with an increase in substrate temperature. The (0 0 3) orientation decreased with increase in (1 0 4) orientation for the films deposited at higher substrate temperatures (>500 °C) indicating that the films’ growth is parallel to the substrate surface. The composition of the experimental films was analyzed using X-ray photoelectron spectroscopy (XPS). The binding energy peaks of Co(2p_3/2) and Co(2p_1/2) are, respectively, observed at 779.3 and 794.4 eV, which can be attributed to the Co³⁺ bonding state of LiCoO₂. The electrochemical measurements were carried out on Li//LiCoO₂ cells with a lithium metal foil as anode and LiCoO₂ film as cathode of 1.5 cm² active area using a Teflon home-made cell hardware. The Li//LiCoO₂ cells were tested in the potential range 2.6-4.2 V. Specific capacity as high as 205 mC/cm² μm was measured for the film grown at 700 °C. The growth of LiCoO₂ films were studied in relation to the deposition parameters for their effective utilization as cathode materials in solid-state microbattery application.     

Synthesis and characterization of a novel polymer electrolyte based on acrylonitrile/N-[4-(aminosulfonyl)phenyl]acrylamide copolymers

<正>Acrylonitrile/N-[4-(aminosulfonyl)phenyl]acrylamide(AN/ASPAA) copolymers were synthesized and used as a host of lithium ion conducting electrolytes.The composition,molecular weight and molecular weight distribution of AN/ASPAA copolymers were determined,and the influence of copolymer composition on the glass temperature of AN/ASPAA copolymers and the ion conductivity of electrolytes were investigated.The molecular weights of AN/ASPAA copolymers were lower than those of AN and ASPAA homopolymers due to the cross-termination reaction.The glass temperatures of AN/ASPAA copolymers increased as the molar fraction of ASPAA units in copolymers increased.The lithium ion conductivities of the polymer electrolytes increased initially as the molar fraction of ASPAA units in copolymers increased,and a maximum conductivity was achieved when the molar fraction of ASPAA in the copolymer was 16.8%.     

Spectral theory for algebraic combinations of Toeplitz and composition operators

We determine the essential spectra of algebraic combinations of Toeplitz operators with continuous symbol and composition operators induced by a class of linear-fractional non-automorphisms of the unit disk. The operators in question act on the Hardy space H² on the unit disk. Our method is to realize the C^*-algebra that they generate as an extension of the compact operators by a concrete C^*-algebra whose invertible elements are easily characterized.