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Recently, significant effort has been made toward the development of graphene-based visible-ligh-responsive photocatalysts and their application to dye wastewater treatment. Herein, a series of octahedral ZnFe2O4/graphene (ZnFe2O4-G) nanocomposites were synthesized using a one-pot solvothermal reaction without the need of a surfactant as novel bifunctional materials exhibiting both high adsorption and good visible-light-responsive photocatalyst properties. The crystal structure, morphology and photocatalytic degradation properties, as well as adsorption behavior, of the octahedral ZnFe2O4/graphene composites were investigated in detail. The adsorption capacity and UV–vis spectrometry results indicate that the dye removal efficiency over the samples followed the order of: methylene blue (MB) > rhodamine B (RhB) > methyl orange (MO). The ZnFe2O4-G materials exhited enhanced photocatalytic degradation properties for cationic dyes (MB and RhB) compared to those for the anionic dye (MO). In addition, the experimental results indicate that the ZnFe2O4-G materials can decompose H2O2 in the visible-light photocatalytic process to form hydroxyl radicals (•OH), which are mainly responsible for the photodegradation of the organic contaminants.

We characterize the hypercyclicity of weighted composition operators on the weighted little Bloch space B 0 α , α > 0 .

Let S ( D ) be the collection of all holomorphic self-maps on D of the complex plane C , and C φ the composition operator induced by φ ∈ S ( D ) . We obtain that there are no hypercyclic composition operators on the little Bloch space B 0 and the Besov space B p .

Density functional theory (DFT) calculations were performed to investigate oxygen adsorption on Mo2C(001) and (201)surfaces at different coverage. The energies and structures of oxygen from lowest to saturated coverages were clearly identified on each surface. Thermodynamics method was introduced to reveal the roles of temperature, pressure as well as oxygen sources (O2, H2O and CO2) on the surface oxygen coverage, which is related to the surface oxidation. On the basis of phase diagram, we can easily identify the stable oxygen coverage at different defined conditions. In addition, it reveals that O2 is the strongest oxidant, which results in the full coverage of oxygen on both surfaces in a wide range of temperature and pressure. Then, H2O and CO2 are weaker oxidants, which could only cause partial oxidation of Mo2C surfaces. These results indicate the facile oxidation of Mo2C catalyst. The possible ways to avoid surface oxidation are keeping higher temperature and H2 pressure in the gas phase.

Monomial Toeplitz operators T z p z ¯ q on the weighted Bergman space of the unit ball in C n are natural extension of the weighted shift operators. In higher dimensions, dim ker ⁡ T z p z ¯ q = ∞ may occur for non-trivial case, thus complex symmetric phenomena will appear. In this paper, we completely characterize when the monomial Toeplitz operator T z p z ¯ q on the weighted Bergman space is J A -symmetric, where J A f ( z ) = f ( A z ‾ ) ‾ with the symmetric unitary n × n matrix A. Moreover, we also determine all possible forms of A such that T z p z ¯ q is J A -symmetric. As an application, we construct the weakly closed unital commutative algebra generated by complex symmetric Toeplitz operators.

We discuss the frequent hypercyclicity and hypercyclicity of multiples of the linear fractional composition operators on A α p and give equivalent conditions of the frequent hypercyclicity and hypercyclicity. We also characterize disjoint hypercyclicity and disjoint mixing behavior of finitely many linear fractional composition operators on the weighted Bergman spaces A α p .

In the present paper, we investigate the disjoint mixing property of finitely many linear fractional composition operators acting on the space of holomorphic functions on the unit ball in C N , and generalize parts of the results obtained by Bes, Martin and Peris in 2011.

In this paper, we give a sufficient condition for the existence of a common universal subspace for various countable families of universal sequences of linear operators. Besides, we show that if σ p ( T ⁎ ) = ∅ , the unitary orbit of the supercyclic operator T contains a path of operators whose closure contains the entire unitary orbit with the strong operator topology, and yet every nonzero vector in the linear span of the orbit of a given supercyclic vector is a common supercyclic vector for the entire path.

We characterize disjoint mixing and disjoint hypercyclicity of finite many composition operators acting on the Hardy space on the unit ball.

In this paper, we study the boundness and compactness of differences of weighted composition operators from the Bloch space B to the space H ∞ of bounded analytic functions on the open unit ball of C n . Moreover, we estimate the norm and the essential norm of differences of composition operators from B to H ∞ .

Let g be a holomorphic function of the unit ball B in the n-dimensional complex space, and denote by T g the extended Cesaro operator with symbol g. Starting with a brief introduction to well-known results about Cesaro operator, we investigate the boundedness and compactness of T g from generally weighted Bloch spaces B log α ( 0 α ∞ ) to Zygmund space Z in the unit ball, and also present some necessary and sufficient conditions.

Let Un be the unit polydisc of ℂn and φ = ( φ 1 , * , φ n ) a holomorphic self-map of Un. This paper shows that the composition operator C φ induced by φ is bounded on the little Bloch space β 0 * ( U n ) if and only if φ l ∈ β 0 * ( U n ) for every l = 1 , 2 , * , n , and also gives a sufficient and necessary condition for the composition operator C φ to be compact on the little Bloch space β 0 * ( U n ) .

Titanium dioxide of the rutile phase has been synthesized using titanium tetrachloride and hydrochloric acid by means of microwave hydrothermal method. The mixture solution is processed in microwave hydrothermal autoclave first at 120 °C for 1.5 h and then at 180 °C for 1 h to precipitate rutile powders. It was revealed that well-dispersed and shuttle-like rutile TiO2 with the average diameter of 10 nm was formed by means of XRD and TEM.